A solution of probabilistic FEM for elastic-plastic materials is pre-sented based on the incremental theory of plasticity and a modified initial stressmethod. The formulations are deduced through a direct differentiation scheme. Par-tial differentiation of displacement, stress and the performance function can be it-eratively performed with the computation of the mean values of displacement andstress. The presented method enjoys the efficiency of both the perturbation methodand the finite difference method, but avoids the approximation during the partial dif-ferentiation calculation. In order to improve the efficiency, the adjoint vector methodis introduced to calculate the differentiation of stress and displacement with respectto random variables. In addition, a time-saving computational method for reliabilityindex of elastic-plastic materials is suggested based upon the advanced First OrderSecond Moment (FOSM) and by the usage of Taylor expansion for displacement. Thesuggested method is also applicable to 3-D cases.
