In this paper, two kinds of simplified constitutive integral algorithm are adopted to solve the problem of isotropic plastic damage under three-dimensional stress state based on the Lemaitre damage model. The solving program compiled by the MATLAB was applied to analyze the failure process of materials under different stress states, and then, the accuracy and efficiency of two algorithms were compared. The numerical simulation shows that both the results of two integral algorithms agree well with theoretical solutions, and are capable to the analysis of damage and fracture of a three-dimensional structure under complex stress state. Compared to the updating algorithm that couples the stress and damage, the weak coupling algorithm that decoupling stress updating and damage in incremental step can better improve the computational efficiency.