A solution of probabilistic FEM for elastic-plastic materials is presented based on the incremental theory of plasticity and a modified initial stress method. The formulations are deduced through a direct differentiation scheme. Partial differentiation of displacement, stress and the performance function can be iteratively performed with the computation of the mean values of displacement and stress. The presented method enjoys the efficiency of both the perturbation method and the finite difference method, but avoids the approximation during the partial differentiation calculation. In order to improve the efficiency, the adjoint vector method is introduced to calculate the differentiation of stress and displacement with respect to random variables. In addition, a time-saving computational method for reliability index of elastic-plastic materials is suggested based upon the advanced First Order Second Moment (FOSM) and by the usage of Taylor expansion for displacement. The suggested method is also applicable to 3-D cases. Liu Ning et al.: Reliability of Elasto-Plastic Structure Using FEM 67 perturbation SFEM, but avoids the approximation in the partial differentiation calculation. In the late 80's, the Neumann expansion technique was introduced, associated with the Monte-Carlo simulation, to obtain the formulation of SFEM. One can refer, for example, to Shinozuka and Deodatis [6] and Yamazaki and Shinozuka [7]. In addition to the methods mentioned above, other sophisticated methods of stochastic finite elements have also been proposed, for example, the response surface method suggested by Faravelli Is], the weighted integral method suggested by Takada[ 9] and the matrix formulation of SFEM suggested by Kiureghian [1~ as well as the innovative methods suggested by Vanmarcke and Shinozuka [11], Hisada and Noguchi [12], Liu and Kiureghian [13], Haldar and Zhou [14], Papadrakakis and Papadopoulos [15], which, among many others, should be mentioned.Most of the studies concerning with SFEM are, however, within the scope of linear elastic problems. Materials such as soil, soft or joint rock, however, exhibit a nonlinear stress-strain relationship. It is obvious that the stochastic response of this kind of materials can not be handled by linear SFEM. The main difficulties are as follows: (1) both element and global stiffness matrices of elastic-plastic materials involve not only the elastic modulus, but also stress and strength parameters; (2) during each loading step, not only the mean value but also the gradients of stress and strain need to be obtained by some iterative algorithms; and (3) for the elastic problem, when using elastic SFEM to calculate the reliability index, only one iterative algorithm is necessary for searching of the design point (Madsen, Krenk and Lind[161). However, for the elastic-plastic problem, two kinds of iterative computations axe needed, it is hence difficult to obtain an efficient iterative algorithm for the two parts. Some attempts have been made to deal with materials whose properties are...