As just stated in a recent question and answer, you can't inherit from a static class. How does one enforce the rules that go along with static classes inside VB.NET? Since the framework is compatible between C# and VB it would make sense that there would be a way to mark a class static, but there doesn't seem to be a way.
Module == static class
If you just want a class that you can't inherit, use a NotInheritable class. But it won't be static/Shared. You could mark all the methods, properties, and members as Shared, but that's not strictly the same thing as a static class in C# since it's not enforced by the compiler.
If you really want the vb.net equivalent to a C# static class, use a Module. It can't be inherited and all members, properties, and methods are static/shared.
Almost there. You've got to prevent instantiation, too.
NotInheritable Class MyStaticClass ''' <summary> ''' Prevent instantiation. ''' </summary> Private Sub New() End Sub Public Shared Function MyMethod() As String End Sub End Class