How to mock ModelState.IsValid using the Moq framework?

You don’t need to mock it. If you already have a controller you can add a model state error when initializing your test:

// arrange
_controllerUnderTest.ModelState.AddModelError("key", "error message");

// act
// Now call the controller action and it will 
// enter the (!ModelState.IsValid) condition
var actual = _controllerUnderTest.Index();