To study the influences of carbody vertical stiffness on vehicle ride quality, a vertical model of railway passenger vehicles, which includes the carbody flexible effects and all vertical rigid modes, is built. With the model and the covariance method, the requirements for the carbody bending frequency are researched. The results show that when the stiffness of a carbody decreases to certain frequencies there are significant vibrations in the carbody, although structural damping provided by a fully equipped carbody will help attenuate the vibration to some extent. A simple way to avoid resonant vibration is to increase the bending frequencies of a carbody: the higher the vehicle running speed, the higher carbody stiffness could be required. However, there are practical limitations to such an increase and the method used in this study can readily obtain the lowest bending frequency required by vehicle ride quality. Finally, the geometric filtering phenomenon and its influences on the carbody resonant flexural vibration are analysed. Results show that it is this phenomenon rather than the natural vibrations of bogie bounce that most strongly influences the resonant flexural vibration of a railway carbody.