In this paper we examine the three-dimensional response of a class of cylindrical inclusions of infinite length embedded in a layered viscoelastic half-space and subjected to plane waves impinging at an oblique angle with respect to the axis of the inclusion. The cases considered include topographical canyons of arbitrary cross section, buried cavities or unlined tunnels, buried pipelines or lined tunnels, and layered sedimentary basins or valleys. All of these cases are formulated and solved by means of a unified indirect boundary integral method based on the use of moving Green's functions for a layered viscoelastic half-space. Results for the three-dimensional response of canyons, cavities, pipelines and valleys as well as comparisons with previous solutions for simple cases are presented for excitations corresponding to P, SV and SH-waves.