No Linq methods are available prior to .NET V3.5, so you can't use them at all.
But all you have to do is recreate it yourself with a For Each loop:
Dim ArraySides As String() = {"Out Side", "Up Down", "Top Buttom"}
Dim StrSide As String = "This is Out Side"
Dim isAnyOf As Boolean = False
For Each s As String In ArraySides
If StrSide.Contains(s) Then
isAnyOf = True
Exit For
End If
Next
If isAnyOf Then
...
End If