The multisource Weber problem is to locate simultaneously m facilities in the Euclidean plane in order to minimize the total transportation cost for satisfying the demand of n fixed users, each supplied from its closest facility. Many heuristics have been proposed for this problem, as well as a few exact algorithms. Heuristics are needed to solve quickly large problems and to provide good initial solutions for exact algorithms. We compare various heuristics, i.e., alternative location-allocation (Cooper, 1964), projection (Bongartz et al. 1994), Tabu search (Brimberg and Mladenovic 1996), p-Median plus Weber (Hansen, Mladenovic and Taillard, 1996), Genetic Search and several versions of Variable Neighbourhood Search. It is found that most traditional and some recent heuristics give poor results when the number of facilities to locate is large and that Variable Neighbourhood Search gives consistently best results on average, in moderate computing time.