| When implementing a highly nonlinear stress strain model to solve boundary valued problems, one of the major challenges is how to reduce the accumulative error and to maintain the effectiveness of the numerical integration. In general, the conventional explicit algorithm tends to have a lower computational efficiency and a higher accumulative error. In order to deal with these challenges, this paper proposes an improved explicit algorithm combining with the cutting plane method, in which the Dormand and Prince Runge Kutta method is used instead of the forward Euler. Using the highly nonlinear SANICLAY model for structured clay as an example, the convergence, the computational efficiency, and the accuracy of three algorithms, namely the conventional explicit algorithm, the improved explicit algorithm, and the implicit algorithm, are compared via numerical simulations of single element tests. Finally, the improved explicit algorithm is applied to the multi element calculation of tunnel excavation. Compared with the implicit algorithm, the conventional explicit algorithm has a lower computational efficiency and a higher accumulative error. The improved explicit algorithm can greatly improve the computational efficiency and accuracy.