For the purpose of establishing optimization of ship structure, studies were undertaken on nonlinear programing procedures and the elemental computer program was developed by authors, which consists of the SUMT method incorporating the DFP method. As the first step towards whole ship structure, some optimum design analyses for box and I section girders mainly adopted in ship structure were conducted by using this program and discussion of solutions obtained led to conclusions as follows. I. Nonlinear programing procedure can be successfully applied to the problems of structural design, which are usually formulated in nonlinear functions. Despite the solution obtained not always being unique optimum, we can find out the optimum solution applicable to design with sufficient examination of solution. II. Optimum design shapes of box and I section girders in regard to girder length and applied load are presented. Optimum design of these plate girders being fairly affected by the web height, constrained functions against the web height should be carefully selected.