Abstract The CRESST (Cryogenic Rare Event Search with Superconducting Thermometers) dark matter search experiment aims for the detection of dark matter particles via elastic scattering off nuclei in $$\mathrm {CaWO_4}$$ CaWO4 crystals. To understand the CRESST electromagnetic background due to the bulk contamination in the employed materials, a model based on Monte Carlo simulations was developed using the Geant4 simulation toolkit. The results of the simulation are applied to the TUM40 detector module of CRESST-II phase 2. We are able to explain up to $$(68 \pm 16)\,\mathrm {\%}$$ (68±16)% of the electromagnetic background in the energy range between 1 and $$40\,\mathrm {keV}$$ 40keV .