This paper presents a simple and robust algebraic design model for hollow fibre membrane modules used in gas separation. A major rationale for making such a model is that membrane separation is an area of increasing importance, but still there does not yet seem to exist any multicomponent model which is simple and robust enough to be useful in synthesis applications. The presented model has been verified against numerical and experimental results from the literature. The results presented here show that product purity is typically predicted within 2%. Module capacity prediction compares favourably with other models from the literature. It has been shown how the model can be extended to take into account pressure drop on the bore side of the hollow fibers. To our knowledge, this is the first reliable algebraic model for gas membrane separation systems able to handle multicomponent mixtures. The algebraic nature of the model and its simplicity should hereafter make it easier to optimize membrane system structures and operating conditions.