We have developed a theoretical model to predict the modulation transfer function (MTF), the shape of the x-ray quantum noise power spectrum (NPS), and the spatial-frequency-dependent detective quantum efficiency (DQE) of an x-ray phosphor screen. The transfer of energy through the screen is modelled as a series of cascaded stochastic processes assuming that the screen consists of many thin phosphor layers. In this way, the model is able to account for the possibility of secondary-quantum noise and the difference in shape between MTF2 and the x-ray quantum NPS. Modelling a Kodak Min-R screen we were able to predict both the number of light quanta emitted per absorbed x-ray and MTF(f) to better than +/- 5%, and the scintillation efficiency to within 10% of experimentally measured values. The shape of the x-ray quantum NPS is predicted to within +/- 5% for spatial frequencies less than about 6 mm-1 and to within +/- 20% for higher frequencies.