Abstract: The distance traveled by contour wave with artificial wave velocity in a step-time is often inconsistent with the mesh size. Therefore, when the transmission boundary formula is applied, the calculation nodes of transmission boundary are usually represented by finite element nodes through the method of time interpolation or spatial interpolation. In this paper, the transmission boundary interpolation formulas of Lagrange interpolation algorithm, Hermite interpolation algorithm and cubic spline interpolation algorithm are derived, and the influence of different interpolation algorithms on the numerical simulation results of transmission boundary is discussed. Firstly, the numerical and analytical solutions of the incident P/SV wave free field problem in elastic half space are compared, and the influence of three interpolation algorithms on the calculation accuracy is discussed. Then, taking the scattering problem of incident P/SV wave in semi-circular valley terrain as an example, the results obtained by different interpolation algorithms are compared. The numerical results show that: Different interpolation algorithms have significant influence on the numerical simulation results of transmission boundary. Among the three interpolation algorithms, the cubic spline interpolation algorithm has the highest accuracy, followed by Lagrange interpolation algorithm, and the Hermite interpolation algorithm has lower accuracy. Compared with the free field, the results of scattering problem are more affected by three interpolation algorithms, and the results of Lagrange interpolation algorithm and cubic spline interpolation algorithm are similar, while the results of Hermite interpolation algorithm are different. The findings of this study can serve as a scientific foundation for the selection of an appropriate interpolation algorithm when utilizing transmission boundaries to simulate the dynamic reaction process of the site.