SUMMARYA technique that takes into account nonparallel interfaces and lateral inhomogeneities 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 is described. The formulation combines a perturbation method with a semidiscrete finite element technique, providing an approximate treatment of wave propagation in irregular layered media. Consistent transmitting boundaries and other semidiscrete hyperelements as well as Green's functions, already available for regular layered media, can be reformulated within the framework of the method. 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.