Abstract: The lateral uneven site with soft-hard connected media is very common, and its seismic response under strong earthquakes has an important impact on the safety of engineering structures. However, studies have seldom been reported to investigate the seismic response of soft-hard connected sites. Based on the indirect boundary element method combined with the exact dynamic stiffness matrix and Green's functions of uniformly distributed loads, the seismic response of soft-hard connected sites in a layered half-space is solved in time-domain via the fast Fourier inverse transform. In the solution, the model is divided into a harder medium of layered half-space region and a softer medium region, while the wavefield is classified into two parts: free field and scattered field. The diffraction response can be simulated by the Green's function of inclined and horizontal fictitious distributed loads acting on corresponding boundaries, and the free field response can be easily solved by the direct stiffness method. The accuracy of the proposed method is verified, and the convergence of the solution model is tested. Numerical calculations are performed to analyze the influences of medium parameters and soft-hard interface dip angles in the seismic response. The results show that in the soft-hard connected site, the stronger ground motion response occurs in the softer medium region. The existence of an soft-hard interface leads to a sudden change in acceleration response, and its sensitivity is significantly affected by medium parameters and interface dig angles. With the increase of difference in the medium parameters and interface dig angles, the peak ground acceleration increases, the response spectrum curve shows more abundant short-period components, and the amplification effect on bedrock motion is enhanced. The influences of soft-hard interface on the surface seismic response of the site are mainly within twice the thickness of the medium layer outside the interface.