The author's method of design sensitivity analysis of nonlinear coincident buckling load factors and corresponding optimization method of finite dimensional elastic structures are shown to be applicable to a structure with moderately large number of degrees of freedom. The sensitivity formulations are written in general form for coincident buckling load factors including limit points and bifurcation points. Optimum designs are found for a spherical latticed dome subjected to a concentrated load and distributed loads, respectively. The results are compared with those by linear eigenvalue formulation. An approximate optimal solution against nonlinear buckling can be obtained by only scaling the solution under linear eigenvalue formulation even for the case where the effect of prebuckling deformation is very large. It is shown that the proposed method is practically applicable to optimum design with coincident critical points especially for the case of hill-top branching where bifurcation points are located at the limit point. In this case, imperfection sensitivity is not enhanced as a result of optimization. The reduction of maximum load factor due to a minor imperfection is shown to be in the same order as that to a major imperfection. Therefore symmetric imperfection as well as asymmetric imperfection should be considered in estimating the maximum loads.