This code will run existing tools or models that your create:

    Private Sub opentool_Click()
    'Ensure that there are references set to the
    'ESRI GeoprocessingUI Object Library and the
    'ESRI Geoprocessing Object Library.
    'Go to Tools > References to do this

    Dim pUID As New UID
    pUID = "esriGeoprocessingUI.ArcToolboxExtension"

    Dim pATBExt As IArcToolboxExtension
    Set pATBExt = Application.FindExtensionByCLSID(pUID)

    Dim pAtb As IArcToolbox
    Set pAtb = pATBExt.ArcToolbox

    Dim pTool As IGPTool

    '* Use this line for custom tools or models
    '* ========================================
    Set pTool = pAtb.GetToolbyNameString("Model8")

    '* Use this line for existing tools
    '* ================================
    'Set pTool = pAtb.GetToolbyNameString("buffer_analysis")

    Dim pCommand As IGPToolCommandHelper
    Set pCommand = New GPToolCommandHelper
    pCommand.SetTool pTool
    pCommand.Invoke Nothing

    End Sub