Proton radiotherapy can assure a more precise treatment of cancer patients, but is more sensitive to uncertainties than conventional radiotherapy using photons. Therefore, non-invasive in-vivo dose verification is desired. The only clinically applied method for 3D dose verification in proton therapy is positron emission tomography (PET) monitoring. Because of the different underlying physical processes, the dose cannot be deduced directly from the measured PET data. The measured PET data needs to be compared to predicted PET data, generated by simulations. The GATE software provides a useful tool for the simulation of b+-activity induced by proton irradiation. The present work focuses on GATE simulations suitable for the workflow at the MedAustron facility. The implemented modality at MedAustron is an offline PET, i.e. the PET scanner is not located in the treatment room. This thesis investigates which nuclides need to be included in the simulation, and what impact the time structure and biological washout have. Finally, a new simulation approach in GATE, the CrossSectionProductionActor (CS-Actor), was evaluated. To investigate these topics, the b+-activity following the irradiation of a PMMA target and a patient's head were simulated. Also, a full radiotherapy plan was simulated using a modelled human head, based on a CT (computed tomography) scan, as the target. The evaluation of the simulations suggests that for range verification, the simulation of 11C might be sufficient. However, if a higher accuracy is needed, the inclusion of 13N is recommended. The importance of including the irradiation time and biological washout was shown as well. The irradiation time, during which production and decay of nuclides take place simultaneously, is the only aspect not yet included in GATE. An extension of GATE and a further examination of the implemented biological washout model is needed. It was found that the CS-Actor is faster and more accurate than the established Actor that fully relies on a Monte Carlo method, a stochastic numerical technique. Apart from some smaller problems, the CS-Actor could be an applicable alternative. At the moment, the CS-Actor is only available for the simulation of 11C and 15O. Therefore, an extension of the Actor to simulate 13N is desirable.