Improving the energy efficiency of cloud computing systems has become an important issue because the electric energy bill for 24/7 operation of these systems can be quite large. The focus of this paper is on the virtual machine (VM) consolidation in a cloud computing system as a way of lowering daily energy consumption of the system. In contrast to the existing works that assume resource demands of VMs are known and given as scalar variables, this paper treats these demands as random variables with known means and standard deviations. These random variables may be correlated with one another, and there are several kinds of resources which can be performance bottlenecks. Therefore, both the correlation and multiple resource type should be considered. The VM consolidation problem is then formulated as a multi-capacity stochastic bin packing problem. This problem is NP-hard, so we propose a heuristic method to solve the problem efficiently. The simulation results show that, in spite of its simplicity and scalability, the proposed method produces high quality solutions.