The works of this thesis concern the design methodology of Permanent Magnet Synchronous Machine (PMSM) for an electric vehicle application. The first part of this report introduces the context of the study and the problem of design. Then, we have shown that it is necessary to adopt an appropriate design methodology based on the progress of each project in the design process. Thus, we proposed different levels of modeling to identify the optimal machine against the specifications, and then characterize it more finely and optimize. The second part of the report deals with the modeling and optimization of the PMSM. First, an analytical model is employed to evaluate the overall performance of hundreds of machines very quickly. The first calculation is used to select the best machine for the application and then optimize them. Then, the second level of modeling is based on reluctance networks. This model allows finer resolution of the PMSM and also permits to perform optimization. The last part of the report is devoted to the optimization of the PMSM in order to greatly improve performances and meet the specifications.