Given the relevance of cardiac maladies in today's society, investigation driven towards the understanding of how our hearts work has been gaining importance. In this bachelor degree thesis we approach the matter by giving a numerical implementation of the ten Tusscher model of the heart's electrophysiology, a very complete and accurate model, even if it may be more complex and computationally expensive than others. We will also incorporate the model to work with the electrochemical problem for a single cardiac cell and for a cardiac tissue, giving a numerical implementation for both, using the Backward Euler method in the first case and a the Finite element method in the second one.