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Use the Visible Property for the Shape object to turn the visibility of maps on/off. For example, see below.

For more information, please see Help / Surfer Automation Help / Objects / Shape Object. Click on the Visible property.

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Sub Main

Dim Surf As Object
Set Surf = CreateObject("Surfer.Application")
Surf.Visible = True

Set Doc = Surf.Documents.Add
Set Shapes = Doc.Shapes

Set Demo = Shapes.AddPostMap(Surf.Path + "\samples\demogrid.dat")
Dim Overlays As Object
Demo.Overlays(1).Name = "Demo"
Demo.Overlays(1).Symbol.Color = srfColorGreen

Set Sample = Shapes.AddPostMap(Surf.Path + "\samples\sample3.dat")
Sample.Overlays(1).Name = "Sample"
Sample.Overlays(1).Symbol.Color = srfColorBlue

Shapes.SelectAll
Set Sel = Doc.Selection
Sel.OverlayMaps
Sel.DeselectAll

Doc.SaveAs(FileName:=Surf.Path+"\Samples\test.srf")

Shapes.Item(1).Overlays("Sample").Visible = False

Doc.Export(FileName:=Surf.Path+"\Samples\test.jpg", Options:="Width=300, Height=300")

End Sub