The rodent hippocampus is known to exhibit two very characteristics patterns of activity: theta long field potential dominates exploratory behavior and REM sleep periods, sharp waves (SPWs) occur during slow wave sleep and awake inactivity or consummatory behaviors. Many evidences suggest that SPWs are associated with the consolidation of pathways experienced during theta. Supporting this view, forward, and more recently, reverse replay of linear track behavioral sequences have been reported in rodents' hippocampal place cells during SPWs. We demonstrate here that these patterns of reactivation can be successfully reproduced by relying on a computational model of the hippocampus with theta phase precession and synaptic plasticity during theta. Two mechanisms are proposed to initiate SPWs events: random reactivation in presence of rapid irregular subthreshold inputs and place selective cells activations. In 2D navigation environments, rather than observing the perfect replay of experienced pathways, new pathways "experienced during immobility" emerge. This suggests a neural mechanism for shortcut navigation.