The free-boundary, axisymmetric tokamak simulation code TSC is used to model the transport time-scale evolution and positional stability of the Princeton Beta Experiment (PBX). A disruptive thermal quench will cause the plasma column to move inwards in major radius. It is shown that the plasma can then lose axisymmetric stability, causing it to displace exponentially off the midplane, terminating the discharge. The accuracy of the code is verified by modelling several controlled experimental shots in PBX.