This is a variation of the great accepted answer posted by the OP. However, this is for WebForms instead of MVC.  I'm working with the assumption that caseAttachmentModel.Body is a byte[]
Essentially everything is the same except with an additional method that sends the zip out as a Response.
using (var compressedFileStream = new MemoryStream()) {
    //Create an archive and store the stream in memory.
    using (var zipArchive = new ZipArchive(compressedFileStream, ZipArchiveMode.Update, false))         {
     foreach (var caseAttachmentModel in caseAttachmentModels) {
        //Create a zip entry for each attachment
        var zipEntry = zipArchive.CreateEntry(caseAttachmentModel.Name);
        //Get the stream of the attachment
        using (var originalFileStream = new MemoryStream(caseAttachmentModel.Body)) {
                using (var zipEntryStream = zipEntry.Open()) {
                    //Copy the attachment stream to the zip entry stream
                    originalFileStream.CopyTo(zipEntryStream);
                }
            }
        }
    }
    sendOutZIP(compressedFileStream.ToArray(), "FileName.zip");
}
private void sendOutZIP(byte[] zippedFiles, string filename)
{
    Response.Clear();
    Response.ClearContent();
    Response.ClearHeaders();
    Response.ContentType = "application/x-compressed";
    Response.Charset = string.Empty;
    Response.Cache.SetCacheability(System.Web.HttpCacheability.Public);
    Response.AddHeader("Content-Disposition", "attachment; filename=" + filename);
    Response.BinaryWrite(zippedFiles);
    Response.OutputStream.Flush();
    Response.OutputStream.Close();
    Response.End();
}
I would also like to point out that advice given by @Levi Fuller on references in the accepted answer is spot on!