This paper presents a review of the solution techniques most widely used for solving the governing equations for static and dynamic, large deflection, elastic-plastic response of structures. For the transient response, one explicit direct integration method (central differences) and three implicit methods (Houbolt, Newmark Beta, and Wilson) are compared with respect to accuracy and stability. A modal superposition technique is developed and compared to the direct integration methods. It is concluded that the choice of a suitable method depends on the structure and loading involved and on the frequency response desired. For the static response, the available techniques are grouped according to whether they yield exact or approximate solutions to the nonlinear equations. The convergence characteristics for each method are summarized. Although it is concluded that the choice of methods depends on which type of nonlinearity (geometric or material) is most significant, the first-order self-correcting method is recommended as the best method overall for static problems.