In this report a model for the ingrowth of a prosthesis in a bone will be formulated and simulated. First an overview is given of all the biological processes that are part of this healing process and what external factors can influence this process. Then a first mathematical model is presented in which the mechanical stimuli (one of the external factors that can influence the healing process) are neglected. The model is solved by numerical means with both the finite volume method as the finite element method. For the finite element method a short introduction is first given to get familiar with this technique. Results for this model will be presented, followed by a short discussion about the results and a conclusion. Subsequently the previous model is extended to incorporate mechanical stimuli, this is done by combining it with an elasticity equation. A short introduction will also be given to the theory of linear elasticity. The model is then solved using finite element analysis and finally also the results for this extended model will be presented, together with once again a short discussion and conclusion.