The weighted residual method was applied to the problem of scattering and diffraction of plane elastic waves, in the form of SH waves, by a tunnel of arbitrary shape located below the swface of a twodimensional half-space. In order to demonstrate the versatility of the method, it was applied to shallow aod deep circular, elliptical, square, and rotated square tunnels with walls that were harder and denser than the surrounding medium. Resuhs obtained were quite sintilar to those obtained using available closed form solutions. It was shown that significant grouod mution amplifications, with respect to the amplitude of incident waves, occurred on the ground surface in the vicinity of the tunnel. Amplifications were dependent upon the shape and depth of the tunnel and the frequency and angle of incidence of incoming SH-waves. Amplification profiles for the lower frequency incident waves were simple near the tunnel on the surface of the balf-space with peak amplifications that did not vary much from 2, the value expected on the surface of a smooth half-space in the absence of a sub-surfuce discontinuity. As the frequency of the incident waves is increaseil. the amplification profiles near the tunnel became more complicated with peak values exceeding 7 for rotated square shaped tunnels located near the grouod surface.