Although the Hertzian contact theory is widely utilized in railway vehicle simulations with new wheel and rail profiles, the Hertzian contact assumptions would lead to inaccurate contact prediction for severely worn wheel and rail profiles due to their geometric conformity, causing non-elliptical contact shapes as well as pressure distribution. For this reason, various non-Hertzian contact models have been studied for use in vehicle dynamics simulations. Among others, a method proposed by Piotrowski and Kik has gained acceptance in predicting non-elliptical wheel-rail contact for vehicle dynamics simulations. Despite the elegant formulation and its accuracy, detailed online geometric calculation for non-elliptical contact shape is required for all the contact patches at every iteration, along with iterative evaluation of the force-deflection relationship. It leads to computation burdens for use in long-distance vehicle simulations. Therefore, in this study, an off-line based numerical procedure for non-Hertzian contact model is developed and integrated in the quasi-steady railway vehicle motion solver.