Dempster-Shafer theory is a formal framework for reasoning and decision-making under uncertainty. A cornerstone in this formalism is Dempster's rule, which provides a mechanism for combining belief functions representing independent pieces of evidence. This rule has been used extensively in information fusion applications. In this paper, we consider the situation where several agents are located at the nodes of a network and can communicate only with their neighbors. We show that synchronous or asynchronous linear consensus mechanisms can be used to combine the agents' belief functions in a distributed way. After convergence, a consensus state is reached, in which all agents hold the same belief, which is equal to the orthogonal sum of the agents' initial belief functions. Simulation results with a simple distributed classification are reported.