A new algorithm that determines the evolution of a surface eroding under reactive‐ion etching is presented. The surface motion is governed by both the Hamilton–Jacobi equation and the entropy condition for a given etch rate. The trajectories of ‘‘shocks’’ and ‘‘rarefaction waves’’ are then directly tracked, and thus this method may be regarded as a generalization of the method of characteristics. This allows slope discontinuities to be accurately calculated without artificial diffusion. The algorithm is compared with ‘‘geometric’’ surface evolution methods, such as the line‐segment method.