Current methods dealing with the energy efficient wireless network planning problem require a static model. However, bit rate requirements vary and rise over time, users move around and path gain fluctuates. In this paper, robust optimization is applied to deal with demand uncertainty. We present a robust optimization model for the energy-efficient planning of wireless networks and apply cutting planes to reduce the complexity of the model. Furthermore, a case study is performed to compare the robust formulation to its deterministic counterpart and to conventional network planning.