Prova con un blocco di using (pressapoco questo)
codice:
Using fs As FileStream = New FileStream(My.Settings.LogPath &  "\LogFile.txt", _                  FileMode.Open, FileAccess.Read, FileShare.ReadWrite)
  Try
            Dim sr As StreamReader = New StreamReader(fs)
            fs.Seek(0, SeekOrigin.Begin)
            LogFile = sr.ReadToEnd()

 Catch ex As Exception
     System.Diagnostics.Debug.WriteLine(ex.Message)
      System.Diagnostics.Debug.WriteLine(ex.StackTrace)
			RetValue = False
  Finally
	fs.Close()
				
  End Try
End Using