Caching popular contents at the edge of wireless networks has recently emerged as a promising technology to improve the quality of service for mobile users, while balancing the peak-to-average transmissions over backhaul links. In contrast to existing works, where a central coordinator is required to design the cache placement strategy, we consider a distributed caching problem which is highly relevant in dense network settings. In the considered scenario, each Base Station (BS) has a cache storage of finite capacity, and each user will be served by one or multiple BSs depending on the employed transmission scheme. A belief propagation based distributed algorithm is proposed to solve the cache placement problem, where the parallel computations are performed by individual BSs based on limited local information and very few messages passed between neighboring BSs. Thus, no central coordinator is required to collect the information of the whole network, which significantly saves signaling overhead. Simulation results show that the proposed low-complexity distributed algorithm can greatly reduce the average download delay by collaborative caching and transmissions.