A technique that allows for nonparallel interfaces and lateral inhomogeneities in an irregular layered medium is described. The formulation combines a semidiscrete finite-element technique with a perturbation method, providing an approximate treatment of wave propagation in irregular layered media. The procedure treats the irregularities as perturbations with respect to a reference, horizontally-layered, laterally-homogeneous medium and produces approximations of the perturbed wave motion with little additional computation effort. Within the framework of the method, consistent transmitting boundaries and other semidiscrete hyperelements as well as Green’s functions, already available for regular layered media, can be reformulated. The method is relevant in problems of foundation dynamics, ground response to seismic waves and site characterization. Example problems are presented toward evaluation of the effectiveness of the method. / text