An application of the direct boundary element method for solving the response of a linearly elastic half-space with a canyon cut into the surface is presented. This approach uses source solutions for an undamped half-space where the resulting singular integral equations are solved directly without adding any artificial damping. Solutions for the displacements on the canyon surface reveal an artificial resonance phenomenon when solving the exterior problem in the frequency domain. The use of an additional source loading in the boundary element method is shown to eliminate these resonances and yield accurate results. A method for solving the Rayleigh waves generated on the surface of the half-space caused by the canyon is shown.