Current trends in virtualization, green computing, and cloud computing require ever increasing efficiency in consolidating virtual machines without degrading quality of service. In this work, we consider consolidating virtual machines on the minimum number of physical containers (e.g., hosts or racks) in a cloud where the physical network (e.g., network interface or top of the rack switch link) may become a bottleneck. Since virtual machines do not simultaneously use maximum of their nominal bandwidth, the capacity of the physical container can be multiplexed. We assume that each virtual machine has a probabilistic guarantee on realizing its bandwidth Requirements-as derived from its Service Level Agreement with the cloud provider. Therefore, the problem of consolidating virtual machines on the minimum number of physical containers, while preserving these bandwidth allocation guarantees, can be modeled as a Stochastic Bin Packing (SBP) problem, where each virtual machine's bandwidth demand is treated as a random variable. We consider both offline and online versions of SBP. Under the assumption that the virtual machines' bandwidth consumption obeys normal distribution, we show a 2-approximation algorithm for the offline version and improve the previously reported results by presenting a (2 + ε)-competitive algorithm for the online version. We also observe that a dual polynomial-time approximation scheme (PTAS) for SBP can be obtained via reduction to the two-dimensional vector bin packing problem. Finally, we perform a thorough performance evaluation study using both synthetic and real data to evaluate the behavior of our proposed algorithms, showing their practical applicability. © 2012 IEEE.