Using elements of functional analysis and the theory of rays (singularities) the author proves existence theorems for solutions of initial boundary-value problems satisfied by elastic displacements in the two media and for Stonely-like disturbances propagating along a non-flat interface between two linear elastic isotropic media. Among more precise results, we note a relatively exhaustive study of the relations between incident and reflected and refracted waves (singularities) under various conditions of incidence and nature of the incident wave (slow or fast one). The treatment makes use of the ellipticity of the interface region, self-adjoint operators and, for singularities, pseudo-differential operators. For the ray studies the basic system obviously is rewritten in the form of a first-order system.