This thesis is devoted to application of boundary element method to elasto-plastic analysis. Formulation of internal points displacement and stresses along with those for boundary nodes. “Traction recovery method” is employed to extract the boundary stresses. Description of discretization method in boundary element method and different kind of integrals encountered in boundary element method are presented. Regular integrals are evaluated through Gauss quadrature method. Weakly singular integrals in two dimensions are evaluated by a semi-analytical method while weakly singular integrals in three dimensions are evaluated employing element subdivision technique and identities of degenerate cells and elements. Rigid body motion technique is employed to circumvent evaluation of strongly singular integrals. Rate-independent theory of plasticity is employed in which Von Mises yields function and Illyushin’s flow theory are employed for plastic analysis. Isotropic, Kinematic and a mixture of them are incorporated in hardening models. The technique employed to evaluate strongly singular integrals on the domain of the problem is to turn the mentioned integrals into nonsingular boundary integrals. The technique and mathematical representation of it are presented too. Once again “element subdivision technique” is described this time for cells that discretize the problem domain ( in order to evaluate weakly singular integrals on the domain). Mathematical representation of the technique used to evaluate strongly singular integrals on the domain is presented next. Then it is discussed how the boundary element equations are arranged to form a matrix equation. “Stress return” theory and Newton-Raphson iterative scheme for solution of the nonlinear matrix equations are described. Finally an algorithm for solution of elasto-plastic problems is presented which is implemented through a Fortran code. Finally some sample problems are solved using the mentioned code to demonstrate boundary element application to elasto-plastic problems. For the first example, a thick cylinder under internal pressure is solved. Results obtained through present code are compared with previous BEM codes, analytic solution and Finite Element solution results. Perforated plate under extension is the second problem considered. Results of the present code are compared with finite element method and experimental results. A cube under uniaxial extension is the second example considered. Results obtained by the present code are in good agreement with the results from other alternative methods and codes. Keywords: Boundary element method (BEM), ealsto-plastic analysis, linear, nonlinear