In this paper a total incremental method for solving nonlinear system equation due to plasticity of shear deformable plates is presented. The material is assumed to undergo small strains. The von Mises criterion is used to evaluate the plastic zone and elastic perfectly plastic material behaviour is assumed. An initial stress formulation is used to formulate the boundary integral equations. The domain integral due to material nonlinearity is evaluated using a cell discretization technique. Several examples are presented and comparisons are made to demonstrate the validity and the accuracy of the total incremental method to solve the nonlinear system of equation due to plasticity.