It was realized recently that various phenomena, related to the sorption of small molecules in polymer glasses could be described within the framework of a site distribution (SD) model. According to the SD model, non-equilibrium structure of glassy polymer leads to the distribution of sorption energies within the interchain holes. The parameters of the distribution for the given polymer-gas system could be expressed through the polymer-gas characteristics or evaluated from the experimental pressure-concentration isotherms. In this work we show how these parameters could be used to predict the sorption isotherms for gas mixtures. The suppression of solubility of each component by the other components, which is the main feature of mixed sorption by polymer glasses can be described within the SD model through the competitive occupancy of low-energy sorption sites. The clear physical meaning of the energy distribution parameters allows to analyze the role of different factors on the competitive sorption from gas mixtures. The comparison of SD model with the other theoretical approaches are given and new experiments, which could check the validity of our approach are proposed.