We provide a flow level analysis of the offloading capability of D2D technology when devices endowed by caches are moving in the network, within the cell and among cells. We introduce the mobility with respect to the receiving user when we consider D2D communication and with respect to the base station when we consider the classical cellular communication. Due to mobility, the quality of both D2D and cellular communication may change over time which makes the analysis challenging. We describe the system through an exact Markovian model, however, since it does not scale with the number of admissible users we provide a closed form approximation model based on multi-class Processor Sharing queue. Numerical results validate the accuracy of our approximation and show a large offloading potential of D2D when devices are equipped with caches. We also observe that mobility increases offloading capability of D2D communications with respect to the static case.