Cardiac Purkinje cells (PCs) are more susceptible to action potential abnormalities as compared to ventricular myocytes (VMs), which could be associated with their distinct intracellular calcium handling. We developed a detailed biophysical model of a mouse cardiac PC, which importantly reproduces the experimentally observed biphasic cytosolic calcium waves. The model includes a stochastic gating formulation for the opening and closing of ryanodine receptor (RyR) channels, simulated with a Monte Carlo method, to accurately reproduce cytosolic calcium wave propagation and the effects of spontaneous calcium release events. Simulations predict that during an action potential, smaller cytosolic calcium wavelets propagated from the sarcolemma towards the center of the cell and initiated larger magnitude cell‐wide calcium waves via a calcium‐induced‐calcium release mechanism. In the presence of RyR mutations, frequent spontaneous calcium leaks from sarcoplasmic reticulum (SR) initiated calcium waves, which upon reaching the cell periphery produced delayed afterdepolarizations (DADs) via sodium‐calcium exchanger (NCX) and T‐type calcium (ICaT) channel activation. In the presence of isoproterenol‐mediated effects, DADs induced triggered activity by reactivation of fast sodium channels. Based on our model, we found that the activation of either L‐type calcium channels (ICaL), ICaT, sodium‐potassium exchanger (INaK) or NCX is sufficient for occurrence of triggered activity; however, a partial blockade of ICaT or INaK is essential for its successful termination. Our modeling study highlights valuable insights into the mechanisms of DAD‐induced triggered activity mediated via cytosolic calcium waves in cardiac PCs and may elucidate the increased arrhythmogeneity in PCs.