The nanofiltration of the water-ethanol mixture of different compositions at three pressure drops through a nanoporous membrane based on poly(1-trimethylsilyl-1-propyne) has been experimentally and theoretically studied. A mathematical model of the onset of flow has been proposed, and the percolation threshold depending on the physicochemical and geometrical characteristics of the membrane system has been found. The model suggests gradual membrane pore opening with an increase in pressure and alcohol concentration in the mixture and can take account of the distribution of alcohol molecules over the cross section of the membrane pores. The theoretical results agree well with the experimental data.