The Mu2e experiment being constructed at Fermilab will search for the coherent neutrino-less conversion of muons to electrons in the field of an atomic nucleus. Mu2e is designed to achieve a sensitivity four orders of magnitude better than previous experiments to this charged lepton flavor violating process. An essential part of the Mu2e experiment is the aluminum muon stopping target. The stopping target is responsible for the energy loss and capture of the muons to be studied and provides the material in which the muon to electron conversion can emerge by interactions with the target nuclei. In the interplay with the muon beam, the magnetic field and the active detector components such as the straw tube tracker, the muon stopping target significantly affects the achievable sensitivity of the overall Mu2e experiment. We present preliminary results of computational simulation studies carried out to optimize the performance of the muon stopping target.