diff --git a/mem/file.go b/mem/file.go
index 5401a3b..885e554 100644
--- a/mem/file.go
+++ b/mem/file.go
@@ -176,6 +176,9 @@ func (f *File) Read(b []byte) (n int, err error) {
 	if len(b) > 0 && int(f.at) == len(f.fileData.data) {
 		return 0, io.EOF
 	}
+	if int(f.at) > len(f.fileData.data) {
+		return 0, io.ErrUnexpectedEOF
+	}
 	if len(f.fileData.data)-int(f.at) >= len(b) {
 		n = len(b)
 	} else {
diff --git a/memmap_test.go b/memmap_test.go
index 09d8680..47414ab 100644
--- a/memmap_test.go
+++ b/memmap_test.go
@@ -2,6 +2,7 @@ package afero
 
 import (
 	"fmt"
+	"io"
 	"os"
 	"path/filepath"
 	"runtime"
@@ -419,3 +420,32 @@ func TestMemFsDirMode(t *testing.T) {
 		t.Error("FileMode is not directory")
 	}
 }
+
+func TestMemFsUnexpectedEOF(t *testing.T) {
+	t.Parallel()
+
+	fs := NewMemMapFs()
+
+	if err := WriteFile(fs, "file.txt", []byte("abc"), 0777); err != nil {
+		t.Fatal(err)
+	}
+
+	f, err := fs.Open("file.txt")
+	if err != nil {
+		t.Fatal(err)
+	}
+	defer f.Close()
+
+	// Seek beyond the end.
+	_, err = f.Seek(512, 0)
+	if err != nil {
+		t.Fatal(err)
+	}
+
+	buff := make([]byte, 256)
+	_, err = io.ReadAtLeast(f, buff, 256)
+
+	if err != io.ErrUnexpectedEOF {
+		t.Fatal("Expected ErrUnexpectedEOF")
+	}
+}