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In this work, we design a relay caching mechanism to improve the energy efficiency in cellular networks, especially for multimedia applications. We consider a single cell with one or more fixed relay stations (RSs) installed near the cell edge. In our design, RSs can receive and cache demanded multimedia content in the cell. After caching, a RS directly serves the users in its coverage area instead of the base station (BS) to reduce energy consumption. In order to find the optimal policy of when and how to cache, we formulate the problem as a Markov decision process (MDP) and obtain the optimal decision table. The numerical results show that the relay caching can save about 15% of total energy. We also present two heuristic policies that perform very close to the optimal one and have low complexity.