A simple solution method was developed for the countercurrent ideal plug flow model of multicomponent gas separation by permeation that is commonly applied to hollow fiber membrane modules. The solution method is independent of the number of components in the feed gas. The result is an implicit function in a single variable defined as the stage cut. The function is readily solved by the method of damped successive substitution. The method was tested for three cases from the literature and found to be insensitive to the initial guess for stage cuts less than 60%.