In three-dimensional cardiac tissue, the re-entrant waves that sustain ventricular fibrillation rotate around a line of phase singularity or vortex filament. The aim of this study was to investigate how the behavior of these vortex filaments is influenced by membrane kinetics, initial conditions, and tissue geometry in computational models of excitable tissue. A monodomain model of cardiac tissue was used, with kinetics described by a three-variable simplified ionic model (3V-SIM). Two versions of 3V-SIM were used, one with steep action potential duration restitution, and one with reduced excitability. Re-entrant fibrillation was then simulated in three tissue geometries: a cube, a slab, and an anatomically detailed model of rabbit ventricles. Filaments were identified using a phase-based method, and the number, size, origin, and orientation of filaments was tracked throughout each simulation. The main finding of this study is that kinetics, initial conditions, geometry, and anisotropy all affected the number, proliferation, and orientation of vortex filaments in re-entrant fibrillation. An important finding of this study was that the behavior of vortex filaments in simplified slab geometry representing part of the ventricular wall did not necessarily predict behavior in an anatomically detailed model of the rabbit ventricles.