diff --git a/src/Psalm/Checker/FileChecker.php b/src/Psalm/Checker/FileChecker.php
index a6df0d644..61c6955e6 100644
--- a/src/Psalm/Checker/FileChecker.php
+++ b/src/Psalm/Checker/FileChecker.php
@@ -33,7 +33,7 @@ class FileChecker extends SourceChecker implements StatementsSource
     protected $actual_file_path;
 
     /**
-     * @var array<string, string>
+     * @var array<int, string>
      */
     protected $suppressed_issues = [];
 
@@ -497,6 +497,26 @@ class FileChecker extends SourceChecker implements StatementsSource
         return $this->suppressed_issues;
     }
 
+    /**
+     * @param array<int, string> $new_issues
+     *
+     * @return void
+     */
+    public function addSuppressedIssues(array $new_issues)
+    {
+        $this->suppressed_issues = array_merge($new_issues, $this->suppressed_issues);
+    }
+
+    /**
+     * @param array<int, string> $new_issues
+     *
+     * @return void
+     */
+    public function removeSuppressedIssues(array $new_issues)
+    {
+        $this->suppressed_issues = array_diff($this->suppressed_issues, $new_issues);
+    }
+
     public function getFQCLN()
     {
         return null;
diff --git a/src/Psalm/Checker/FunctionLikeChecker.php b/src/Psalm/Checker/FunctionLikeChecker.php
index abba5461d..859449662 100644
--- a/src/Psalm/Checker/FunctionLikeChecker.php
+++ b/src/Psalm/Checker/FunctionLikeChecker.php
@@ -1321,6 +1321,26 @@ abstract class FunctionLikeChecker extends SourceChecker implements StatementsSo
         return $this->suppressed_issues;
     }
 
+    /**
+     * @param array<int, string> $new_issues
+     *
+     * @return void
+     */
+    public function addSuppressedIssues(array $new_issues)
+    {
+        $this->suppressed_issues = array_merge($new_issues, $this->suppressed_issues);
+    }
+
+    /**
+     * @param array<int, string> $new_issues
+     *
+     * @return void
+     */
+    public function removeSuppressedIssues(array $new_issues)
+    {
+        $this->suppressed_issues = array_diff($this->suppressed_issues, $new_issues);
+    }
+
     /**
      * Adds a suppressed issue, useful when creating a method checker from scratch
      *
diff --git a/src/Psalm/Checker/SourceChecker.php b/src/Psalm/Checker/SourceChecker.php
index a0aa52bb5..634b50f1a 100644
--- a/src/Psalm/Checker/SourceChecker.php
+++ b/src/Psalm/Checker/SourceChecker.php
@@ -161,6 +161,34 @@ abstract class SourceChecker implements StatementsSource
         return $this->source->getSuppressedIssues();
     }
 
+    /**
+     * @param array<int, string> $new_issues
+     *
+     * @return void
+     */
+    public function addSuppressedIssues(array $new_issues)
+    {
+        if ($this->source === null) {
+            throw new \UnexpectedValueException('$source cannot be null');
+        }
+
+        return $this->source->addSuppressedIssues($new_issues);
+    }
+
+    /**
+     * @param array<int, string> $new_issues
+     *
+     * @return void
+     */
+    public function removeSuppressedIssues(array $new_issues)
+    {
+        if ($this->source === null) {
+            throw new \UnexpectedValueException('$source cannot be null');
+        }
+
+        return $this->source->removeSuppressedIssues($new_issues);
+    }
+
     /**
      * @return string
      */
diff --git a/src/Psalm/Checker/StatementsChecker.php b/src/Psalm/Checker/StatementsChecker.php
index 59fef1f4d..c60f4bf7f 100644
--- a/src/Psalm/Checker/StatementsChecker.php
+++ b/src/Psalm/Checker/StatementsChecker.php
@@ -129,6 +129,33 @@ class StatementsChecker extends SourceChecker implements StatementsSource
             }
             */
 
+            $new_issues = null;
+
+            if ($docblock = $stmt->getDocComment()) {
+                $comments = CommentChecker::parseDocComment((string)$docblock);
+                if (isset($comments['specials']['psalm-suppress'])) {
+                    $suppressed = array_filter(
+                        array_map(
+                            /**
+                             * @param string $line
+                             *
+                             * @return string
+                             */
+                            function ($line) {
+                                return explode(' ', trim($line))[0];
+                            },
+                            $comments['specials']['psalm-suppress']
+                        )
+                    );
+
+                    if ($suppressed) {
+                        $new_issues = array_diff($suppressed, $this->source->getSuppressedIssues());
+                        /** @psalm-suppress TypeCoercion */
+                        $this->addSuppressedIssues($new_issues);
+                    }
+                }
+            }
+
             if ($stmt instanceof PhpParser\Node\Stmt\If_) {
                 IfChecker::analyze($this, $stmt, $context, $loop_context);
             } elseif ($stmt instanceof PhpParser\Node\Stmt\TryCatch) {
@@ -348,6 +375,11 @@ class StatementsChecker extends SourceChecker implements StatementsSource
                     return false;
                 }
             }
+
+            if ($new_issues) {
+                /** @psalm-suppress TypeCoercion */
+                $this->removeSuppressedIssues($new_issues);
+            }
         }
 
         return null;
diff --git a/src/Psalm/StatementsSource.php b/src/Psalm/StatementsSource.php
index 3db359917..6d05b44a4 100644
--- a/src/Psalm/StatementsSource.php
+++ b/src/Psalm/StatementsSource.php
@@ -82,4 +82,18 @@ interface StatementsSource
      * @return array<int, string>
      */
     public function getSuppressedIssues();
+
+    /**
+     * @param array<int, string> $new_issues
+     *
+     * @return void
+     */
+    public function addSuppressedIssues(array $new_issues);
+
+    /**
+     * @param array<int, string> $new_issues
+     *
+     * @return void
+     */
+    public function removeSuppressedIssues(array $new_issues);
 }
diff --git a/src/Psalm/TraitSource.php b/src/Psalm/TraitSource.php
index ee90435f5..a1ed8c63e 100644
--- a/src/Psalm/TraitSource.php
+++ b/src/Psalm/TraitSource.php
@@ -140,4 +140,22 @@ class TraitSource implements StatementsSource
     {
         return [];
     }
+
+    /**
+     * @param array<int, string> $new_issues
+     *
+     * @return void
+     */
+    public function addSuppressedIssues(array $new_issues)
+    {
+    }
+
+    /**
+     * @param array<int, string> $new_issues
+     *
+     * @return void
+     */
+    public function removeSuppressedIssues(array $new_issues)
+    {
+    }
 }
diff --git a/tests/AssertTest.php b/tests/AssertTest.php
new file mode 100644
index 000000000..711c2a641
--- /dev/null
+++ b/tests/AssertTest.php
@@ -0,0 +1,54 @@
+<?php
+namespace Psalm\Tests;
+
+class AssertTest extends TestCase
+{
+    use Traits\FileCheckerInvalidCodeParseTestTrait;
+    use Traits\FileCheckerValidCodeParseTestTrait;
+
+    /**
+     * @return array
+     */
+    public function providerFileCheckerValidCodeParse()
+    {
+        return [
+            'assertInstanceOfB' => [
+                '<?php
+                    class A {}
+                    class B extends A {
+                        public function foo() : void {}
+                    }
+
+                    function assertInstanceOfB(A $var) : void {
+                        if (!$var instanceof B) {
+                            throw new \Exception();
+                        }
+                    }
+
+                    function assertInstanceOfClass(A $var, string $class) : void {
+                        if (!$var instanceof $class) {
+                            throw new \Exception();
+                        }
+                    }
+
+                    function takesA(A $a) : void {
+                        assertInstanceOfB($a);
+                        $a->foo();
+                    }
+
+                    function takesA(A $a) : void {
+                        assertInstanceOfB($a);
+                        $a->foo();
+                    }',
+            ],
+        ];
+    }
+
+    /**
+     * @return array
+     */
+    public function providerFileCheckerInvalidCodeParse()
+    {
+        return [];
+    }
+}
diff --git a/tests/IssueSuppressionTest.php b/tests/IssueSuppressionTest.php
index 15d607cdd..563ddefcd 100644
--- a/tests/IssueSuppressionTest.php
+++ b/tests/IssueSuppressionTest.php
@@ -4,6 +4,7 @@ namespace Psalm\Tests;
 class IssueSuppressionTest extends TestCase
 {
     use Traits\FileCheckerValidCodeParseTestTrait;
+    use Traits\FileCheckerInvalidCodeParseTestTrait;
 
     /**
      * @return array
@@ -24,6 +25,24 @@ class IssueSuppressionTest extends TestCase
                         }
                     }',
             ],
+            'undefinedClassOneLine' => [
+                '<?php
+                    class A {
+                        public function b() : void {
+                            /**
+                             * @psalm-suppress UndefinedClass
+                             */
+                            new B();
+                        }
+                    }',
+            ],
+            'undefinedClassOneLineInFile' => [
+                '<?php
+                    /**
+                     * @psalm-suppress UndefinedClass
+                     */
+                    new B();',
+            ],
             'excludeIssue' => [
                 '<?php
                     fooFoo();',
@@ -32,4 +51,35 @@ class IssueSuppressionTest extends TestCase
             ],
         ];
     }
+
+    /**
+     * @return array
+     */
+    public function providerFileCheckerInvalidCodeParse()
+    {
+        return [
+            'undefinedClassOneLineWithLineAfter' => [
+                '<?php
+                    class A {
+                        public function b() {
+                            /**
+                             * @psalm-suppress UndefinedClass
+                             */
+                            new B();
+                            new C();
+                        }
+                    }',
+                'error_message' => 'UndefinedClass - src/somefile.php:8 - Class or interface C',
+            ],
+            'undefinedClassOneLineInFileAfter' => [
+                '<?php
+                    /**
+                     * @psalm-suppress UndefinedClass
+                     */
+                    new B();
+                    new C();',
+                'error_message' => 'UndefinedClass - src/somefile.php:6 - Class or interface C',
+            ],
+        ];
+    }
 }