This paper proposes a way to compile a 2D elastic-plastic cohesive zone model based on the cohesive zone element through user-defined material subroutine( VUMAT) in ABAQUS. The delamination of thin plates is studied using the VUMAT subroutine of elastic-plastic cohesive zone model( CZM). The simulation results are compared with the result of the Bilinear CZM,the Polynomial CZM and the experiments. The results show that the cohesive zone models have great influence on the tensile forces in the progress of delamination,and to choose suitable CZMs for the various adhesives bonded joints.