This is a method that will compress a directory of files using the ShellClass and the Shell32 api.

    Public Sub startCompression(ByVal stateInfo As Object)

      Dim strArgs As String = ""
      Dim strdest As String = ""

      '----- Check the file for a .zip extenstion.

      strdest += strDestinationFile
      If System.IO.Path.GetExtension(strdest).ToUpper.EndsWith(".ZIP") = False Then
        strdest += ".zip"
      End If

      If strdest.IndexOf(" ") <> -1 Then
        strdest = """" & strdest & """"
      End If

      '----- Binary Array representing a zip file header.

      Dim emptyZip As Byte() = New Byte() {80, 75, 5, 6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}

      '----- Write out the zip file

      Dim fs As FileStream = File.Create(Me.strDestinationFile)
      fs.Write(emptyZip, 0, emptyZip.Length)
      fs.Flush()
      fs.Close()
      fs = Nothing

      Dim sc As ShellClass = New ShellClass
      Dim src As Shell32.Folder = sc.NameSpace(Me.strSourceDir)
      Dim dst As Shell32.Folder = sc.NameSpace(Me.strDestinationFile)

      '----- Begining File Compression in System Controlled Thread
      dst.CopyHere(src, 20)
      

      '----- Sleep to allow the compression thread to begin execution

      System.Threading.Thread.CurrentThread.Sleep(5000) ' 5 seconds is usually more than enough
    End Sub

There's a GPL library for compression, implemented entirely in managed code.  I've found this library very easy to use in the past.

http://www.icsharpcode.net/OpenSource/SharpZipLib/