Previous research on topology optimization focussed primarily on global structural behaviour such as stiffness and frequencies. However, to obtain a true optimum design of a vehicle structure, stresses must be considered. The major difficulties in stress based topology optimization problems are two-fold. First, a large number of constraints must be considered, since unlike stiffness, stress is a local quantity. This problem increases the computational complexity of both the optimization and sensitivity analysis associated with the conventional topology optimization problem. The other difficulty is that since stress is highly nonlinear with respect to design variables, the move limit is essential for convergence in the optimization process. In this research, global stress functions are used to approximate local stresses. The density method is employed for solving the topology optimization problems. Three numerical examples are used for this investigation. The results show that a minimum stress design can be achieved and that a maximum stiffness design is not necessarily equivalent to a minimum stress design.