The propagation of small‐amplitude stress discontinuities in linear, isotropic, in‐homogeneous viscoelastic media whose behavior is governed by integral stress‐strain laws is considered. The formulation is in terms of creep functions of virtually arbitrary type. A formal ray‐series asymptotic approach is developed which allows for the construction of wavefront solutions given either creep or relaxation functions for the medium. The advantages of these methods for obtaining numerical results are then clearly demonstrated.