Monte Carlo simulations based on the Geant4 simulation toolkit were performed for the carbon wedge degrader used in the beam line at the Center of Proton Therapy of the Paul Scherrer Institute (PSI). The simulations are part of the beam line studies for the development and understanding of the GANTRY2 and OPTIS2 treatment facilities at PSI, but can also be applied to other beam lines. The simulated stopping power, momentum distributions at the degrader exit and beam line transmission have been compared to accurate benchmark measurements. Because the beam transport through magnetic elements is not easily modeled using Geant4a connection to the TURTLE beam line simulation program was made. After adjusting the mean ionization potential of the carbon degrader material from 78 eV to 95 eV, we found an accurate match between simulations and benchmark measurements, so that the simulation model could be validated. We found that the degrader does not completely erase the initial beam phase space even at low degraded beam energies. Using the validation results, we present a study of the usability of beryllium as a degrader material (mean ionization potential 63.7 eV). We found an improvement in the transmission of 30-45%, depending on the degraded beam energy, the higher value for the lower energies.