Reducing the energy consumption of data centers and the Cloud is very important in order to lower CO_2 footprint and operational cost (OPEX) of a Cloud operator. To this extent, it becomes crucial to minimise the energy consumption by consolidating the number of powered-on physical servers that host the given virtual machines (VMs). In this work, we propose a novel approach to the energy efficient VM consolidation problem by applying Robust Optimisation Theory. We develop a mathematical model as a robust Mixed Integer Linear Program under the assumption that the input to the problem (e.g. resource demands of the VMs) is not known precisely, but varies within given bounds. A numerical evaluation shows that our model allows the Cloud Operator to tradeoff between the power consumption and the protection from more severe and unlikely deviations of the uncertain input.