This study is concerned with an application of the Boundary Element Method to 2-dimensional elastoplastic stress analysis on the material nonlinearities. The boundary integral formulation adopted an initial stress equation in the inelastic term. In order to determine the initial stress increment, the increment of initial elastic strain energy due to elastic increment in stressstrain curve was used as the convergence criterion during iterative process. For the validity of this procedure, the results of B.E.M. with constant elements and NISA with linear elements where compared on the thin plate with 2 edge v-notches under static tension and the thick cylinder under internal pressure. And this paper compared the results of using unmedical integral with the results of using semi-analytical integral on the plastic domain integral.