In this article we present a generalized theoretical model for the continuous separation of particles using the pinched flow fractionation method. So far the theoretical models have not been able to predict the separation of particles without the use of correction factors. In this article we present a model which is capable of predicting the separation from first principles. Furthermore we comment on the importance of the incorporation of the finite height of the micro fluidic channels in the models describing the system behavior. We compare our model with the experiment obtained by Seki et al. (J. Takagi, M. Yamada, M. Yasuda and M. Seki, Lab Chip, 2005, 5, 778-784).