Abstract: The twin shear strength theory and unified strength theory proposed by Yu Mao-hong in 1983 and 1990 respectively are extended to be used as a general unified elasto plastic constitutive model in this paper. This unified elastoplastic constitutive model has been implemented in a elastoplastic finite element computational program and applied to the elastic plastic analysis of engineering structures.Unified strength theory(failure criterion) and its associated elastoplastic constitutive model and unified elastic plastic computational progam include the wellknown strength theories and some new possible strength theories. It can be adapted for most kinds of materials, and used for the elasto plasic analysis and limit analysis of engineering structures. The engineering use of this unified strength theory, unified elasto plastic constitutive model and unified elasto plastic computational program can raise high the utilization ratio of mainals, reduce the investment and produce huge economic effect.