Fast proliferation of mobile Internet and high-demand mobile applications necessitates the introduction of different priority classes in next-generation cellular networks. This is especially crucial for efficient use of radio resources in the heterogeneous and virtualized network environments. Despite the fact that many analytical tools have been proposed for capacity and radio resource modelling in cellular networks, only a few of them explicitly incorporate priorities among services. We propose a novel analytical model to analyse the performance of a priority-based cellular CDMA system with finite source population. When the cell load is above a certain level, low-priority calls may be blocked to preserve the quality of service of high-priority calls. The proposed model leads to an efficient closed-form solution that enables fast and very accurate calculation of resource occupancy of the CDMA system and call blocking probabilities, for different services and many priority classes. To achieve them, the system is modelled as a continuous-time Markov chain. We evaluate the accuracy of the proposed analytical model by means of computer simulations and find that the introduced approximation errors are negligible.