A mathematical model for high-flux asymmetric hollow fibre membrane was developed considering the effect of permeate pressure build-up inside the fibre bore. A new solution technique was developed to solve the model equations, which constitute a boundary value problem. The ordinary differential equations were solved as an initial value problem in two successive steps using the Gear's BDF method. The technique is advantageous since it requires minimum computational time and effort with improved solution stability, and the computational complexity does not multiply as the number of components increases. The model predictions and the robustness of the numerical technique were validated with experimental data for several membrane systems with different flow configurations. The model and the solution technique were applied to evaluate the separation characteristics of air using representative membranes with different configurations, including single-stage, single-stage with permeate recycle, single-stage with retentate recycle, air blending, and two stages in series. The study demonstrates that the new solution technique can conveniently handle the high-flux hollow fibre membrane problems with different module configurations.