The aim of this work is to interpret experimental findings of Stokes and Schlarb on the basis of analytical formulas and finite element calculations. In the analytical approach, some simplifications that had to be made proved to be inappropriate. Only computer calculations may reveal the details of the processes involved in vibration welding. Comparison of the computer calculations with the experiments reveals that even transient effects in viscosity have to be considered. Viscosity is dependent not only on temperature and shear rate, but also on the frequency or amplitude of vibration. After correction for these effects, the correlation between theory and experiments proved to be excellent. Based on the calculations, some recommendations are presented to improve weld quality, as ascertained by the type of fracture in a tensile test, by changing the welding parameters.