diff --git a/src/SharpCompress/Common/EntryStream.cs b/src/SharpCompress/Common/EntryStream.cs
index e4de4ca9..d265be00 100644
--- a/src/SharpCompress/Common/EntryStream.cs
+++ b/src/SharpCompress/Common/EntryStream.cs
@@ -79,11 +79,25 @@ public class EntryStream : Stream, IStreamStack
         {
             if (ss.BaseStream() is SharpCompress.Compressors.Deflate.DeflateStream deflateStream)
             {
-                deflateStream.Flush(); //Deflate over reads. Knock it back
+                try
+                {
+                    deflateStream.Flush(); //Deflate over reads. Knock it back
+                }
+                catch (NotSupportedException)
+                {
+                    // Ignore: underlying stream does not support required operations for Flush
+                }
             }
             else if (ss.BaseStream() is SharpCompress.Compressors.LZMA.LzmaStream lzmaStream)
             {
-                lzmaStream.Flush(); //Lzma over reads. Knock it back
+                try
+                {
+                    lzmaStream.Flush(); //Lzma over reads. Knock it back
+                }
+                catch (NotSupportedException)
+                {
+                    // Ignore: underlying stream does not support required operations for Flush
+                }
             }
         }
 #if DEBUG_STREAMS
@@ -111,11 +125,25 @@ public class EntryStream : Stream, IStreamStack
         {
             if (ss.BaseStream() is SharpCompress.Compressors.Deflate.DeflateStream deflateStream)
             {
-                await deflateStream.FlushAsync().ConfigureAwait(false);
+                try
+                {
+                    await deflateStream.FlushAsync().ConfigureAwait(false);
+                }
+                catch (NotSupportedException)
+                {
+                    // Ignore: underlying stream does not support required operations for Flush
+                }
             }
             else if (ss.BaseStream() is SharpCompress.Compressors.LZMA.LzmaStream lzmaStream)
             {
-                await lzmaStream.FlushAsync().ConfigureAwait(false);
+                try
+                {
+                    await lzmaStream.FlushAsync().ConfigureAwait(false);
+                }
+                catch (NotSupportedException)
+                {
+                    // Ignore: underlying stream does not support required operations for Flush
+                }
             }
         }
 #if DEBUG_STREAMS
diff --git a/tests/SharpCompress.Test/Zip/ZipReaderTests.cs b/tests/SharpCompress.Test/Zip/ZipReaderTests.cs
index c3b53e11..0ad07ffb 100644
--- a/tests/SharpCompress.Test/Zip/ZipReaderTests.cs
+++ b/tests/SharpCompress.Test/Zip/ZipReaderTests.cs
@@ -444,4 +444,50 @@ public class ZipReaderTests : ReaderTests
             Assert.Equal(archiveKeys.OrderBy(k => k), readerKeys.OrderBy(k => k));
         }
     }
+
+    [Fact]
+    public void EntryStream_Dispose_DoesNotThrow_OnNonSeekableStream_Deflate()
+    {
+        // Test for issue: EntryStream.Dispose() should not throw NotSupportedException
+        // when Flush() fails on non-seekable streams (Deflate compression)
+        var path = Path.Combine(TEST_ARCHIVES_PATH, "Zip.deflate.dd.zip");
+        using Stream stream = new ForwardOnlyStream(File.OpenRead(path));
+        using var reader = ReaderFactory.OpenReader(stream);
+        
+        // This should not throw, even if internal Flush() fails
+        while (reader.MoveToNextEntry())
+        {
+            if (!reader.Entry.IsDirectory)
+            {
+                using var entryStream = reader.OpenEntryStream();
+                // Read some data
+                var buffer = new byte[1024];
+                entryStream.Read(buffer, 0, buffer.Length);
+                // Dispose should not throw NotSupportedException
+            }
+        }
+    }
+
+    [Fact]
+    public void EntryStream_Dispose_DoesNotThrow_OnNonSeekableStream_LZMA()
+    {
+        // Test for issue: EntryStream.Dispose() should not throw NotSupportedException
+        // when Flush() fails on non-seekable streams (LZMA compression)
+        var path = Path.Combine(TEST_ARCHIVES_PATH, "Zip.lzma.dd.zip");
+        using Stream stream = new ForwardOnlyStream(File.OpenRead(path));
+        using var reader = ReaderFactory.OpenReader(stream);
+        
+        // This should not throw, even if internal Flush() fails
+        while (reader.MoveToNextEntry())
+        {
+            if (!reader.Entry.IsDirectory)
+            {
+                using var entryStream = reader.OpenEntryStream();
+                // Read some data
+                var buffer = new byte[1024];
+                entryStream.Read(buffer, 0, buffer.Length);
+                // Dispose should not throw NotSupportedException
+            }
+        }
+    }
 }