This paper proposes an analytical study of 3D beamforming for 5G wireless networks. In a first step, we develop a three dimensional analytical beamforming model for wireless networks. This 3D model enables in particular, to focus analyzes to the specific zone covered by an antenna beam. This 3D beamforming model is validated by comparison with Monte Carlo simulations: the two approaches give very close SINR (Signal to Interference plus Noise Ratio) values. Thanks to this model, it becomes easy to quantify the impact of 3D beamforming in terms of performance, quality of service and coverage in a future 5G wireless network. Different scenarios are presented, which quantify the impact of the 3D beamforming wireless network and show the accuracy of the model. The proposed model is then used to compare 2D and 3D beamforming and to show the interest of exploiting the third dimension.