Studying calcium dynamics in cardiac cells is crucial for uncovering the causes of cell failure. A key factor in heart failure is the perturbation of the calcium-induced-calcium-release (CICR) cycle. This cycle involves complex interactions between the cytoplasm and the sarcoplasmic reticulum via various channels and biochemical species. The perturbation in CICR could be explained by pathological behavior of ionic channels especially the ryanodine receptor (RyR). In this study, we present a computational modeling of the interaction of calcium dynamics in a medium including the sarcolemma and sarcoplasmic reticulum. The governing equations consists of a nonlinear reaction-diffusion system that describes the different calcium fluxes and their buffers in the two media. In the first, we describe the mathematical model. To realize the numerical simulation of our model, we proceed by a finite element discretization and then we choose an appropriate resolution algorithm. Finally, we show the numerical results obtained.