AbstractAn indirect boundary integral method to obtain the three‐dimensional response of an infinitely long, layered, viscoelastic valley of arbitrary cross‐section embedded in a layered viscoelastic half‐space is presented. The valley is excited by homogeneous plane waves impinging at an oblique angle with respect to the axis of the valley. The method and associated computer programs are tested by comparison with available results in the limiting two‐dimensional case of incidence normal to the axis of the valley. Additional comparisons with previous three‐dimensional results obtained by a hybrid finite element‐boundary integral method for cylindrical valleys subjected to obliquely incident waves show large differences. However, the results obtained here for an infinitely long valley appear to be in some agreement with earlier results for an elongated prolate semi‐ellipsoidal valley and with results obtained by a discrete wavenumber boundary element approach. An extensive bibliography on the dynamic response of valleys is a