The influence of surface roughness and contact adhesion on the rolling behaviour of dry particles has been investigated. Rough particle surfaces are approximated using an array of spheres, the properties of which are informed by random processes. An analytical model has been derived by considering the torques that a particle experiences. Two mechanisms of rolling resistance are explored – a stationary particle experiencing a tangential force, and a dynamically rolling particle. The analytical model is found to agree well with simulations of the equivalent system using the discrete element model. Adhesive forces are found to increase rolling resistance in all cases. The complex consequences of varying the height variance and length scale of the surface roughness are reproduced accurately by the analytical model.