An analysis of the scattering of steady-state SH waves by a shallow buried unlined elliptical tunnel is presented. For the horizontal boundary, a mirror method in elliptic coordinates is proposed, which is implemented using the Mathieu function addition theorem. Taking into account the stress-free condition of the tunnel, an infinite equation system was created and solved after truncating it. The orientation of the tunnel is arbitrary, and typical calculations are performed for tunnels arranged horizontally and vertically in the long axis. The effects of depth, the ellipse’s axis ratio, and wavenumber on the dynamic stresses around the tunnel are investigated.