Abstract: The elastic model of discontinuous deformation computational mechanics developed by the authors is extended to elasto plastic model.The elasto plastic behavior of the multi body system is duly taken into consideration in addition to the discontinuous characteristics of interfaces and contacts between different bodies.Based on the parametric variational principle of minimum potential energy for different materials,the mathematical formulation of the nonlinear discontinuous deformation system is established and the corresponding solving algorithm is developed for elasto plastic analysis.The problem of interaction of foundation beam and rock base with different material characteristics is analyzed to illustrate the applications of the proposed method.The results have shown that the proposed method couples the nonlinear behavior of materials with discontinuous features of interaction of multi body system and can simulate the complex behavior of interaction effect of multiple bodies with different characteristics.This method might be a powerful numerical computational tool for geotechnical engineering problems.