A method is described for calculating the two-dimensional trajectory of a vertically or horizontally unstable axisymmetric tokamak plasma in the presence of a resistive vacuum vessel The vessel is not assumed to have toroidal symmetry. The plasma is represented by a current-filament loop that is free to move vertically and to change its major radius. Its position is evolved in time self-consistently with the vacuum vessel eddy currents. The plasma current, internal inductance, and poloidal beta can be specified functions of time so that eddy currents resulting from a disruption can be modeled. The vacuum vessel is represented by a set of current filaments whose positions and orientations are chosen to model the dominant eddy current paths. Although the specific application is to the Tokamak Fusion Test Reactor, the present model is of general applicability.