Alternative finite element representations employing stress based element formulations are described for the solution of static/dynamic nonlinear stress analysis problems. In particular, this work investigates the proposed formulations as applied to both static and dynamic situations involving material nonlinearity. The formulations eliminate the need to employ numerical integration in evaluating the stiffness matrix and the residual force vector. Some noteworthy aspects via the present formulations include independence of element integral computations from nonlinearities, introduction of boundary conditions in a direct and natural manner and the applicability to general situations. Numerical test cases are described to validate the present formulations for finite element computations. The overall results show good accuracy and improvement in efficiency for the computations.