Abstract: Viscoelastic artificial boundary elements are commonly applied in the analysis of semi-infinite wave propagation problems, which can accurately absorb the scattered waves generated in the calculation domain. However, the mass density, the stiffness and the damping coefficient of the viscoelastic artificial boundary element are different from those of the internal domain. Therefore, the instability often occurs in the boundary region when the explicit time-domain stepwise integration is performed in the overall model, so, the calculation efficiency of the explicit integral for the overall system is affected. Currently, there is no effective solution to this problem which remains to be settled to conduct efficient large-scale wave propagation simulation. For the two dimensional viscoelastic artificial boundary element, we establish the edge subsystem and corner subsystem which can represent the typical characteristics of the overall system, by the analysis method of transfer matrix spectral radius based on the central difference format commonly used, we derive the analytical solutions of the stability conditions of the edge subsystem and corner subsystem. After that, we analyze the influence of various physical parameters of the two dimensional viscoelastic artificial boundary element on the stability conditions, and obtain the method for improving the stability condition of the explicit algorithm by increasing the mass density of the viscoelastic artificial boundary element. The homogeneous and layered half-space examples show that, set the mass density of the internal element as the upper limit of the mass density of the viscoelastic artificial boundary element, the method proposed in this paper can effectively improve the numerical stability of the explicit time-domain integration when using the viscoelastic artificial boundary elements, without affecting the calculation accuracy, and the calculation efficiency can be significantly improved in the explicit dynamic analysis. The model size (distance from the scattered wave source to the artificial boundary) has a little effect on the stability of the explicit integral which can be ignored.