One of the biggest unknowns of our Universe is the nature of dark matter. The existence of dark matter was proven by many astrophysical and cosmological observations and it is known that it constitutes 27 % of the energy budget of our Universe. Many theories were proposed to explain the nature of the dark matter which may be a particle. In order to detect dark matter particles, there are three dierent mechanisms: production, indirect searches and direct searches. Direct searches look for recoils in a detector induced by the scatter o of a dark matter particle. There are dierent types of direct search experiments focusing on dierent mass ranges. In the past years, the attention was extended towards possible low mass dark matter particles. In this mass range, the leading experiment is CRESST. The CRESST experiment uses scintillating CaWO4 crystals as target while simultaneously measuring the scintillation light with a light detector and the phonon excitation of the crystal lattice with a thermometer. It is able to dierentiate between dierent types of particle interactions. CRESST focuses its search eorts for dark matter in the O(100MeV=c2) mass region. In order to be able to detect possible dark matter particles in this mass region, CRESST can measure recoil energies down to O(100 eV). However, in this energy region, beta and gamma particles are hardly distinguishable from nuclear recoils which makes the search for a possible dark matter signal very dicult. These beta and gamma particles originate from radioactive backgrounds inside and outside the target crystal. Since it is not possible to remove all of this background physically, it is vital to have a background model predicting the contributions of these backgrounds to the region of interest. In order to do this, simulations based on the Geant4 framework are used. In this thesis, the electromagnetic background of CRESST is studied and simulated. Based on this model, the overall background is decomposed into contributions from individual sources, their isotopic compositions and locations. The validity of the model is assessed in comparison with the experimental data recorded in-situ with the detector module TUM40 of CRESST-II Phase 2. In this rst full Monte Carlo study of electromagnetic backgrounds in CRESST, we were able to successfully reproduce (75 19) % of the observed backgrounds in this detector module. Furthermore, we decomposed the background into three basic components: internal contamination of CaWO4, both radiogenic and cosmogenic, and contamination of external copper parts. Finally, we discussed the implication of these ndings on the CRESST experiment and outline possible future improvements.