AbstractWe aim to enhance the stability of finite element models of dynamic structural contact with multiphase granular soils which are described by advanced soil plasticity models that can simulate monotonic and cyclic behaviour of multiphase soils. Often, numerical oscillations cannot be avoided in these contact models and can cause advanced soil models to significantly overshoot stress, leading to unrealistic discontinuities in the stress paths. This situation can challenge the stability of the stress integration scheme and the global finite element solver and lead to the early termination of the analysis. We specifically address the issue of stress overshooting by presenting novel solutions and the corresponding stress integration schemes for a representative soil model for unsaturated granular soils. Also, several examples are provided to evaluate the integration scheme and show the advantages and limitations of the proposed overshooting solutions in solving a contact-impact problem involving unsaturated granular soils.