SUMMARY. The extracellular epicardial potential fields produced by simple depolarization waves in the in situ canine left ventricular myocardium were analyzed. A mathematical model that included tissue anisotropy was developed to explain the observed fields. Values of intracellular (i), extracellular (o), longitudinal (f), and transverse (t) resistivity which gave the best fit between the model and experimental data were (in ohm-cm, mean ± SD): r,,, = 852 ± 232, r,,, = 1247 ± 210, r,, = 291 ± 38, rii = 1677 ± 331. The potential fields around simple stimulated waves on the epicardium can best be explained if the extracellular wavefront voltage is (mean ± SD) 74 ± 7 mV for a wave propagating parallel to the local muscle fibers, and 43 ± 6 mV for a wave propagating perpendicular to these fibers. We conclude that the anisotropy of the electrical conductivity of cardiac muscle has important effects on the propagation of waves of depolarization and on the potential fields produced by depolarization in the intact heart. (Circ Res 50: 342-351, 1982)