Multi-beam antenna systems are the basic technology used in developing fifth-generation (5G) mobile communication systems. In practical implementations of 5G networks, different approaches are used to enable a massive multiple-input-multiple-output (mMIMO) technique, including a grid of beams, zero-forcing, or eigen-based beamforming. All of these methods aim to ensure sufficient angular separation between multiple beams that serve different users. Therefore, ensuring the accurate performance evaluation of a realistic 5G network is essential. It is particularly crucial from the perspective of mMIMO implementation feasibility in given radio channel conditions at the stage of network planning and optimization before commercial deployment begins. This paper presents a novel approach to assessing the impact of a multi-beam antenna system on an intra-cell interference level in a downlink, which is important for the accurate modeling and efficient usage of mMIMO in 5G cells. The presented analysis is based on geometric channel models that allow the trajectories of propagation paths to be mapped and, as a result, the angular power distribution of received signals. A multi-elliptical propagation model (MPM) is used and compared with simulation results obtained for a statistical channel model developed by the 3rd Generation Partnership Project (3GPP). Transmission characteristics of propagation environments such as power delay profile and antenna beam patterns define the geometric structure of the MPM. These characteristics were adopted based on the 3GPP standard. The obtained results show the possibility of using the presented novel MPM-based approach to model the required minimum separation angle between co-channel beams under line-of-sight (LOS) and non-LOS conditions, which allows mMIMO performance in 5G cells to be assessed. This statement is justified because for 80% of simulated samples of intra-cell signal-to-interference ratio (SIR), the difference between results obtained by the MPM and commonly used 3GPP channel model was within 2 dB or less for LOS conditions. Additionally, the MPM only needs a single instance of simulation, whereas the 3GPP channel model requires a time-consuming and computational power-consuming Monte Carlo simulation method. Simulation results of intra-cell SIR obtained this way by the MPM approach can be the basis for spectral efficiency maximization in mMIMO cells in 5G systems.