Seismic exploration is the primary tool for mapping out hydrocarbon deposits. In forward modeling, subsurface structures are assumed to be known, and the task is to simulate elastic wave propagation throughout the medium. Inversion programs then update subsurface assumptions in order to reconcile the model response with actual measurements. In collaboration with Royal Dutch Shell, we have found that RBF-FD (radial basis function generated finite difference) spatial discretization offers outstanding accuracy and algebraic simplicity for modeling elastic wave propagation, especially in layered media that feature large numbers of irregularly curved interfaces.