A mathematical analysis is presented for a simplified model of cross-flow in tubular membranes, for which a numerical treatment was recently reported. It is shown, step by step, that by using several asymptotic and analytical techniques the number of dimensionless numbers governing the problem can be reduced. Results are derived in terms of algebraic or integral equations, with accuracy comparable to those obtained from the complicated numerical solution. The analysis performed here permits an improved insight into the structure of the problem, compared to the numerical technique, and facilitates explanation of the numerically obtained results. The present approach can, in principle, be generalized for application to more complicated models of the particular process.