A method to compute the aerodynamics of multi-element aerofoil, high-lift systems is outlined. The Reynolds-averaged Navier-Stokes equations are solved using an unstructured-grid approach, together with a finite-volume spatial discretisation and a dual-time implicit, time-marching solution procedure. Turbulence modelling is at the differential Reynolds stress level, in order to capture the anticipated influence of significant streamline curvature on the flow development, particularly for landing configurations. Results are presented comparing predictions with experimental data from the UK’s National High-Lift Programme. In general, good agreement is obtained but further work is required to incorporate transition prediction which appears to have an influence on the stall mechanism.