In this paper, a complete sensitivity analysis of the optimal parameters for the axial flux permanent magnet synchronous machines working in the field weakening region is implemented. Thanks to the presence of a parameterized accurate analytical model, it is possible to obtain all the required parameters of the machine. The two goals of the ideal design are to maximize the power density: P-density and the ratio of maximal to rated speed: n(max)/n(r,) which is an inductance related parameter keeping the efficiency at the target speed above 90%. Different slots/poles/phases combinations are studied to reveal the optimum combination for each phase. This paper has studied the effect of the ratio of number of stator slots to number of rotor poles on the P-density and n(max)/n(r). It is shown that a low value of this parameter results in a better P-density and n(max)/n(r). The effect of the outer diameter, and the inner to outer diameter ratio are studied with respect to the two design goals. In addition, a comparison between the finite and the theoretical infinite speed designs is implemented. A complete 3D finite element validation has proven the robustness of the analytical model.