The Multi-Commodity Capacitated Multi-facility Weber Problem (MCMWP) is concerned with locating I capacitated facilities in the plane to satisfy the demand of J customers for K commodities with the minimum total transportation cost. The MCMWP is a non-convex optimization problem. Customer locations, demands and capacities for each commodity are known a priori. The transportation costs, which depend on the commodity type, are proportional to the distance between customers and facilities. We first present a branch and bound algorithm then we propose a beam search heuristic for the MCMWP. According to our computational experiments on randomly generated test instances, we can say that the proposed beam search heuristic yields comparable results with the previous best heuristics.