Numerous studies have explored the effect of sleep on memory. It is well known that a period of sleep, compared to a similar period of wakefulness, protects memories from interference, improves performance, and might also reorganize memory traces in a way that encourages creativity and rule extraction. It is assumed that these benefits come from the reactivation of brain networks, mainly involving the hippocampal structure, as well as from their synchronization with neocortical networks during sleep, thereby underpinning sleep-dependent memory consolidation and reorganization. However, this memory reorganization is difficult to explain within classical memory models. The present paper aims to describe whether the influence of sleep on memory could be explained using a multiple trace memory model that is consistent with the concept of embodied cognition: the Act-In (activation-integration) memory model. We propose an original approach to the results observed in sleep research on the basis of two simple mechanisms, namely activation and integration.