As one approach towards the optimization of ship structures, such stiffened structures as bulk-heads, side and bottom shells are considered. Stiffened structures are transposed into flat grillages composed of straight orthogonal beams laterally loaded and their optimum design analyses are conducted by using framed structure analysis and nonlinear programming. The relationships between loaded area, beam number and optimum arrangements of beam sections in both simplified grillages and the bottom grillages of oil tankers are discussed. Conclusions obtained are as follows : I. The combination of matrix force method for framed structure analysis and nonlinear programming (here, SUMT method in corporating DFP method is used) can be successfully applied to the optimum design of grillages. II. In design of grillages, as the number of beams increases, the weight of grillages increases.Furthermore, the weight in case of grillages is larger than that in case of single beam structure. III. Optimum arrangements of beam sections in simplified grillages are such that shorter beams with large sectional area hang longer beams with small sectional area, still more in case where total load is applied only shorter beams, longer beams are not necessary. IV. Optimum arrangements in the bottom grillages of a center tank of oil tankers are a little different from in case of simplified grillages because of bottom platings working as a part of longitudinal and transverse girders and of difference in allowable stress between longitudinal and transverse girders.