A frequency domain boundary element method is introduced in this paper to simulate the scattering of two-dimensional Rayleigh waves by a cavity on the surface of an elastic half-space. This numerical method allows the Rayleigh wave to escape the truncated boundary without producing any spurious reflections. The numerical results of the displacements and stresses of a 2-D Rayleigh wave which travels along a flat surface of an elastic half-infinite medium are in good agreement when compared with theoretical ones. The problem of a Rayleigh wave scattering by a cavity on the surface of an elastic half-infinite medium is simulated by the proposed numerical method. The result is taken as the benchmark to introduce an approximate analytical method for such problems of scattering by a cavity on the surface. This numerical method is formulated for a two-dimensional homogeneous, isotropic, linearly elastic half-space and its implementation in a frequency domain boundary scheme is discussed in detail.