A novel modelling approach to predict the influence of road texture on the rolling resistance of car tyres is presented where the large static tyre deformations and the small texture induced tyre vibrations are treated separately. The energy dissipation due to the large continuous cyclic deformation of the tyre cross section for a treadless tyre subject to nominal load on a smooth road is determined in a non-linear steady-state rolling analysis on an FEM tyre model. The additional energy dissipation resulting from the contact forces and tyre vibrations due to the combined effect of the tread profile and the road texture, are determined based on a modal representation of the deformed tyre. The predicted rolling resistance coefficients are compared to experimental data. Although an offset in the absolute rolling resistance levels can be observed, the model predicts the correct trend regarding the increase of rolling resistance with increasing texture depth.