The dissipative rolling friction moment in a simple belt-drive system is estimated both experimentally and computationally while taking into account the detachment events at the belt-pulley interface. Shear traction is estimated based on measurements of the shear strain along the contact arc. It is shown that the dissipative moment can be approximated by taking the difference between the shear traction and the load carried by the belt. A model is developed for analyzing the contributions of different components to this dissipative moment by considering both the volumetric and surface hysteresis losses. The computed rolling friction moment is found to be in good agreement with that estimated based on the experiments. It is also found that while the shear- and stretching-induced energy losses contribute the most to the dissipation in the belt drive system, the losses associated with the Schallamach waves of detachment make up a considerable portion of the dissipation in the driver case.