diff --git a/src/net/http/fs.go b/src/net/http/fs.go
index 51b6b1d32f..773e74d536 100644
--- a/src/net/http/fs.go
+++ b/src/net/http/fs.go
@@ -33,6 +33,27 @@ import (
 // An empty Dir is treated as ".".
 type Dir string
 
+// mapDirOpenError maps the provided non-nil error from opening name
+// to a possibly better non-nil error. In particular, it turns OS-specific errors
+// about opening files in non-directories into os.ErrNotExist. See Issue 18984.
+func mapDirOpenError(originalErr error, name string) error {
+	if os.IsNotExist(originalErr) || os.IsPermission(originalErr) {
+		return originalErr
+	}
+
+	parts := strings.Split(name, string(filepath.Separator))
+	for i := range parts {
+		fi, err := os.Stat(strings.Join(parts[:i+1], string(filepath.Separator)))
+		if err != nil {
+			return originalErr
+		}
+		if !fi.IsDir() {
+			return os.ErrNotExist
+		}
+	}
+	return originalErr
+}
+
 func (d Dir) Open(name string) (File, error) {
 	if filepath.Separator != '/' && strings.ContainsRune(name, filepath.Separator) {
 		return nil, errors.New("http: invalid character in file path")
@@ -41,9 +62,10 @@ func (d Dir) Open(name string) (File, error) {
 	if dir == "" {
 		dir = "."
 	}
-	f, err := os.Open(filepath.Join(dir, filepath.FromSlash(path.Clean("/"+name))))
+	fullName := filepath.Join(dir, filepath.FromSlash(path.Clean("/"+name)))
+	f, err := os.Open(fullName)
 	if err != nil {
-		return nil, err
+		return nil, mapDirOpenError(err, fullName)
 	}
 	return f, nil
 }
diff --git a/src/net/http/fs_test.go b/src/net/http/fs_test.go
index 17a0e4a9af..8ff2faf9b9 100644
--- a/src/net/http/fs_test.go
+++ b/src/net/http/fs_test.go
@@ -1161,6 +1161,39 @@ func TestLinuxSendfileChild(*testing.T) {
 	}
 }
 
+// Issue 18984: tests that requests for paths beyond files return not-found errors
+func TestFileServerNotDirError(t *testing.T) {
+	defer afterTest(t)
+	ts := httptest.NewServer(FileServer(Dir("testdata")))
+	defer ts.Close()
+
+	res, err := Get(ts.URL + "/index.html/not-a-file")
+	if err != nil {
+		t.Fatal(err)
+	}
+	res.Body.Close()
+	if res.StatusCode != 404 {
+		t.Errorf("StatusCode = %v; want 404", res.StatusCode)
+	}
+
+	dir := Dir("testdata")
+	_, err = dir.Open("/index.html/not-a-file")
+	if err == nil {
+		t.Fatal("err == nil; want != nil")
+	}
+	if !os.IsNotExist(err) {
+		t.Errorf("err = %v; os.IsNotExist(err) = %v; want true", err, os.IsNotExist(err))
+	}
+
+	_, err = dir.Open("/index.html/not-a-dir/not-a-file")
+	if err == nil {
+		t.Fatal("err == nil; want != nil")
+	}
+	if !os.IsNotExist(err) {
+		t.Errorf("err = %v; os.IsNotExist(err) = %v; want true", err, os.IsNotExist(err))
+	}
+}
+
 func TestFileServerCleanPath(t *testing.T) {
 	tests := []struct {
 		path     string