A hybrid approach was developed to compute the dose deposited in cancerous and healthy tissues during stereotactic synchrotron radiation therapy treatment. The proposed approach divides the computation into two parts: (1) the dose deposited by primary radiation (coming directly from the incident X-ray beam) is calculated using a deterministic algorithm based on ray casting, optimized for transport in voxelized geometries; (2) the dose deposited by secondary radiation (Rayleigh and Compton scattering, fluorescence) is computed using a hybrid algorithm combining Monte Carlo and deterministic calculations. In the Monte Carlo part, a set of scattering and fluorescence events occurring in the patient is determined. These events are further processed in a deterministic way, which considerably improves the statistics of the final dose map. The results obtained in test cases are compared to those obtained with the Monte Carlo method alone (Geant4 and MCNPX codes) and found to be in excellent agreement. The proposed simulation scheme makes it possible to simulate dose maps with a single PC, featuring computation time and statistical fluctuations substantially reduced in comparison with full Monte Carlo simulations.