Slow and discontinuous action potential (AP) conduction through non-uniform junctions in cardiac tissue is generally considered unsafe and pro-arrythmogenic. We study AP conduction through the Purkinje-ventricular junction (PVJ) and determine relationships between the tissue structure, conduction velocity and safety. The 3D wedge model has been developed earlier to incorporate details of the transmural AP heterogeneity, tissue geometry and fibre orientation of the canine left ventricular free wall [1], as well as detailed electrophysiological properties of the canine Purkinje fiber (PF) cells [2]. In the model, a single PF was penetrating the 3D ventricular wedge from the endocardium; the intercellular diffusion coefficients in the PF and ventricular tissues (0.8 and 0.2 mm²/s) were set to produce the AP conduction velocities of ~1.8 and 0.5 m/s [3], respectively. Thickness, d, and the diffusion coefficient, D, of the PF were varied in order to determine optimal conditions (velocity, v, and safety factor, SF) of the AP conduction through the PVJ. The AP conduction from PF through the anatomically and electrically non-uniform PVJ was discontinuous with a time delay of ~5 ms, as seen in experiments [3, 4]. Dependence of SF on d showed a maximum at ~1 mm, and dependence of SF on v had a maximum at ~0.3 m/s, which corresponded to an optimal velocity providing the maximum safety of AP conduction through the PVJ. Dependence of SF on D showed a maximum at ~0.6 mm²/s, and the respective dependence of SF on v in this case also had a maximum at ~0.3 m/s. At the ionic level, long AP conduction time delays enhanced the electrical source-to-load mismatch at the PVJ, but at the same time allowed a larger amount of the charge provided by the membrane ionic currents to be stored at the cell capacity and then passed through the PVJ over time. In summary, both very fast and very slow AP conduction is unsafe, and there is an optimal velocity providing the maximum SF of conduction through the PVJ. Respective conduction time delay allows the tissue to accumulate and pass through the junction sufficient charge, but is not long enough for the source-to-load mismatch at the PVJ to be enhanced in time.