An optimal design strategy is developed for the Bridgman crystallization process through the formulation of a nonlinear program. The objective function and constraints are designed to optimize the conditions for the growth of crystals with nearly flat melt-crystal interfaces. The decision variables are the temperatures of the hot and cold zones, the size of the thermal barrier, and the thickness of the crucible. The equations for momentum and energy transport in the melt, for conduction in the crystal and crucible, and the energy balance at the melt-crystal interface are solved using finite elements. The nonlinear program is solved using the controlled random search technique. Results are presented for the growth of GaAs crystals.