In this theoretical study, the membrane-supported interfacial polymerization is distinctively considered as a Poisson process. We liken the film formation on the supporting membrane to the phenomenon that numerous water-waves created by raindrops hitting a pond expand on the pond surface gradually as they grow larger. Accordingly, a mathematical equation for the permeability of thin-film composite membranes, named as "Poisson Interfacial Polymerization" equation, is proposed. And the simulation results are in good agreement with the corresponding experimental results reported by many researchers. We believe that our approach offers new degrees of freedom in establishing mathematical models for interfacial polymerization. (c) 2013 Elsevier B.V. All rights reserved.