An algorithm is presented to design the microscopic morphology of structural materials from the macroscopic mechanical properties in consideration of the material and geometrical nonlinearities. A maximization and minimization problems of macroscopic external potential energy are defined with a constraint to the volume fraction of the microscopic material phases. Then the optimality criteria method is employed to solve the problems and the nonlinear homogemzation method is also used to obtain the macroscopic stresses caused by the macroscopic strain histories.