Abstract <p>A modified grid-characteristic method for modeling elastic wave propagation in heterogeneous media with an explicit description of material interfaces is presented. The approach is based on implicit and explicit-implicit numerical schemes that ensure stability and accuracy at large time steps and small spatial steps in elongated domains. Contact conditions between the materials are properly formulated in the form of reflected and refracted waves or by modifying the system of equations for an implicit scheme. Numerical results are presented for one- and two-dimensional problems, including the modeling of waves propagating through multilayer structures and laminated glasses. The order of convergence is estimated for various schemes. The results show that the developed method is able to provide high modeling accuracy and describe complex wave patterns in heterogeneous media.</p>