Sharing economy is a transformative socio-economic phenomenon built around the idea of sharing underused resources and services, e.g. transportation and housing, thereby reducing costs and extracting value. Anticipating continued reduction in the cost of electricity storage, we look into the potential opportunity in electrical power system where consumers share storage with each other. We consider two different scenarios. In the first scenario, consumers are assumed to already have individual storage devices and they explore cooperation to minimize the realized electricity consumption cost. In the second scenario, a group of consumers is interested to invest in joint storage capacity and operate it cooperatively. The resulting system problems are modeled using cooperative game theory. In both cases, the cooperative games are shown to have non-empty cores and we develop efficient cost allocations in the core with analytical expressions. Thus, sharing of storage in cooperative manner is shown to be very effective for the electric power system.