A method of optimizing the fissile fuel distribution to obtain minimum critical mass for a fast breeder reactor of fixed power is presented. Constraints on the power density and on the fuel enrichment are considered. The reactor is described by one-group diffusion theory. The optimal trajectory in the phase space (flux-current) is found a priori using the Maximum Principle of Pontryagin. It is shown that in general, the optimum reactor has three distinct regions: a central constant-power-density region, a region of maximum fuel enrichment and an outer region of minimum enrichment corresponding to the blanket. The existence of this last region and its dimension depend on the outer boundary condition which can simulate the presence of an external reflector. The expressions obtained for the optimized dimensions of each region can be solved analytically and numerical results are given.