The acoustic radiation of vibrating bodies can usually be considered as a linear phenomenon as in most cases the vibration amplitudes of oscillating bodies are small compared to their dimension. However, in case of large amplitude and small Mach number, the large displacement amplitude of a vibrating body gives rise to geometric nonlinear acoustic effects. In this paper it is shown that the nonlinearity causes an asymmetry in the time signal of the radiated pressure as observed at a fixed position, resulting in harmonic distortion of the radiated sound field. These nonlinear effects can be analysed by the finite element method, using a linear fluid behaviour in combination with a moving mesh approach. This approach is implemented and used to predict the nonlinear sound radiation of lithographic stages oscillating at large amplitude and low Mach number. Acoustic experiments prove the validity of the analysis technique for the geometrical nonlinear phenomena. In addition the structural response of a nearby body excited by the nonlinear acoustic radiation of the stage is calculated and verified experimentally.