An analytical model, describing the flux of reactive-gaseous species surviving transit through a cylindrical reactor with apertures at either end, is developed. The magnitude of the surviving flux is evaluated as a function of the reaction probability of the wall, which may be discontinuous from point-to-point within the reactor, and of the relative dimensions of the vessel. Numerical solutions were obtained for vessels with values of the ratio length–radius in the range 2–6. The model is compared with a simplified approximation that is particularly applicable for reactor geometries with small values of length–radius.