This thesis deals with topology optimization of structures with out-of –plane geometrical nonlinearity under static lateral loading. The structures analysed contain the elements with in-Plane and out-of-plane behavior. The Green-Lagrange deformation tensor is employed for the mathematical modeling of geometrical nonlinearity. The equilibrium equations are solved using a piece-wise linear incremental model. The Rosen method, as a feasible direction method, has been utilized for the optimization procedure. The sensitivity analysis has been performed through both an exact and an approximate differentiation scheme. A finite difference approach has been employed to obtain the approximate sensitivities. Parallel processing has been used to reduce sensitivity calculation time. A power-law approach has been utilized to obtain a black and white topology. Two norms of displacements as well as a norm based on the complementary elastic work are considered as the objective functions. The obtained results show that there is a little difference between the linear and nonlinear topologies, except for the cases that the norm of global displacements is minimized. The examples also show that the obtained topologies are not much sensitive to the time step length required in the non-linear solution. Moreover it is found that the norm of in-plane displacements is not suitable for such a topology optimization and thus the problem is sensitive to the objective function used.