An exercise machine with a two directional pivoting user support assembly has a user support or platform which supports the user and pivots about a first pivot axis during an exercise movement, and is also pivotable about at least one second pivot axis to involve the user's core muscles in balancing and maintaining the user support in a stable position. A manually operable locking device with a simple flip switch lever is provided for selectively locking the user support against rotation about the second pivot axis, so that the user can easily chose whether to perform the exercise with a stable support or to add a level of difficulty by using the unstable seat mode and exercising core muscles during the exercise.