Calcium dynamics plays a central role in studying the excitation-contraction coupling process which allows cardiac muscle cells to pump blood through the heart and around the body. In this presentation, we model such calcium movements by solving a system of nonlinear reaction-diffusion equations. A number of researchers found that calcium concentration is extremely sensitive to the volume and shape of the cell and to the transverse tubule (T-tub) in the cell. We predict calcium behavior in an ideal model and in two more realistic models by employing a meshless method and a finite element method. Currently, it still takes hours to model a single cycle of the excitation-contraction process with only a few realistic t-tubules, however improvements in the computational technique will enable more complex and detailed investigations of heart muscle disease.