Abstract: Based on the wave theory of saturated frozen soil medium, the scattering problem of plane P wave incident on the concave terrain of saturated frozen soil half-space is studied by using the Fourier-Bessel series expansion method of wave function. Through numerical examples, the influence of physical and mechanical parameters such as incident frequency, incident angle, temperature (ice content), porosity and contact parameters on the surface displacement amplitude is analyzed when the plane P wave is incident on the half-space concave terrain of saturated frozen soil. The results show that the temperature (ice content) has a significant effect on the surface displacement amplitude at different depth-width ratios and incident frequencies. Under different depth-width ratios, the semi-circular depression terrain is more sensitive to temperature changes than the shallow circular depression terrain. At low frequency, the vertical displacement decreases with the increase of incident angle, and the horizontal displacement increases with the increase of incident angle. The horizontal displacement decreases with the increase of porosity, but the porosity has little effect on the vertical displacement. With the increase of the incident wave frequency, the spatial distribution of the displacement amplitude in the half-space depression terrain of saturated frozen soil is more complicated. As the frequency continues to increase, the change of displacement amplitude with the incident angle is no longer obvious, while the influence of porosity gradually increases, especially in shallow circular concave terrain, the increase of porosity leads to more sensitive displacement amplitude. In addition, at lower temperature (T=−0.7°C), the displacement amplitude of the concave terrain surface changes significantly with the contact parameters, while at higher temperature (T=−0.3°C), the horizontal displacement and vertical displacement do not change significantly.