Scattering of surface waves by a two-dimensional cavity, which is on the free surface of an elastic half-space, is theoretically investigated in the current paper. It is shown that the expressions for the scattered field displacements are derived in an elegant approach by using the reciprocity theorem and the decomposition technique that decomposes the total field into incident and scattered fields. The displacements of the scattered field then can be analytically obtained by the reciprocity theorem. The achieved solutions are verified by the Boundary Element Method (BEM) modeling of two-dimensional wave propagation in elastic half-spaces that applies a truncation of the in finite boundary to account for the contribution of the omitted part. The comparisons of displacements are graphically displayed and show the agreements between analytical and numerical results.