The importance of using sophisticated interface models to obtain realistic numerical solutions of soil–structure interaction (SSI) problems has been recognised in recent decades. With this aim, various advanced interface models have been developed, which assume that the same advanced constitutive model can describe the soil behaviour inside and outside the shear zone. These models fail to adequately address the experimentally observed stick–slip transition, assuming permanent sticking between the soil and structure. Furthermore, the influence of interface roughness requires model parameter adjustments, e.g., in the critical state of the soil, which are questionable from a physical point of view. To overcome these shortcomings, we propose a general relationship to describe the evolution of the shear strain in the shear zone as a function of the surface roughness, the density, and the normal stress. This relationship, which assumes a stick–slip transition at the interface, can be combined with an advanced constitutive model to describe soil–structure interface behaviour using the same set of model parameters as for the surrounding soil. Depending on the surface roughness of the interface, this transition leads to a localisation within the soil in the shear zone (for rough surfaces) or at the contact surface (for smooth surfaces). The proposed model was validated using interface shear tests from the literature on dry granular soils. A hypoplastic constitutive model was used in the simulations. The comparison of experimental and calculated results demonstrates the ability of the proposed model to realistically reproduce shear stress and relative displacements, including the stick–slip transition observed in the experiments. This instils confidence in the model’s reliability and accuracy, thus providing a reliable numerical tool for SSI analyses.