The ring cyclotron of the Paul Scherrer Institute (PSI) accelerates an intense proton beam from 72MeV up to 590MeV. This happens in four cavities of very high quality factor, oscillating in the fundamental mode. The beam can excite parasitic oscillation modes (HOMs), because of its time structure. Measurements showed that their field can leak out into the vacuum chamber. Until now, there is no tool available to predict the potentially harmful effect of these HOMs onto the beam operation of the cyclotron. It is foreseeable that these effects might play a role if even higher beam currents have to be accelerated. This dissertation therefore deals with the numerical analysis and measurement of beam-cavity interactions. First calculations for a single cavity, interacting with a proton bunch were performed with MAFIA's eigenmode- (E3), time domain- (T3) and particle-in-cell (TS3) solvers. However, the structured grid and the limited computing performance of MAFIA make realistic simulations impossible. A simplified computation method is developed in this dissertation since a self-consistent simulation is impossible on today's computers: The parallel eigensolver Omega3P of the Stanford Linear Accelerator Center (SLAC) allowed us to calculate eigenmodes of the entire ring cyclotron for the first time ever. The rf fields are expanded onto a superposition of these modes and the excitation is calculated in frequency domain. Trajectories of the particles in the static magnetic field, superposed with the space charge fields and the beam excited HOMs, are then simulated. However, the quantitative accuracy of this model is still limited. On the one hand, because of the simplification in the geometry of the simulated rf structure, which otherwise would lead to a problem size going beyond the available computing resources. On the other hand, because it is not yet possible to simulate strongly absorbing boundaries more accurately. The simulation results confirm that up to proton beam currents of 2mA, corresponding to the routinely accelerated beam intensities, only a small deformation of the charge distribution appears. This thesis leads to a new simulation tool for further studies of intensity increases in high power cyclotrons.