The role of cardiac tissue anisotropy in the breakup of vortex filaments is studied using two detailed cardiac models. In the Beeler-Reuter model, modified to produce stable spiral waves in two dimensions, we find that anisotropy can destabilize a vortex filament in a parallelepipedal slab of tissue. The mechanisms of the instability are similar to the ones reported in previous work on a simplified cardiac model by Fenton and Karma [Chaos 8, 20 (1998)]. In the Luo-Rudy model, also modified to produce stable spiral waves in two dimensions, we find that anisotropy does not destabilize filaments. A possible explanation for this model-dependent behavior based on spiral tip trajectories is offered. (c) 2001 American Institute of Physics.