AbstractA numerical procedure has been developed for the design of shock‐free supercritical airfoil sections with an allowance for viscous effects, provided the boundary layer is fully attached over the airfoil. The method described combines, in an interative process, an inviscid hodograph‐based inverse‐design algorithm (IDA) developed by the author and the inverse‐boundary layer algorithm (LTBLCEQL) by Miner, Anderson and Lewis. Here, the subcritical portion of the inviscid solution is obtained by solving the full stream function equation in a computational plane which is a conformal map of the two‐sheeted hodograph plane. For the supercritical portion, a characteristics calculation is carried out in the hodograph plane. Viscous effects are then incorporated via the displacement surface concept. A Crank–Nicolson type implicit finite difference scheme is utilized to solve the laminar and turbulent boundary layer equation which are expressed in Levy–Lees variables. A transition model allowing for gradual, rather than instantaneous, transition to turbulent flow is also incorporated. The numerical coupling procedure is applied to the design of two airfoil sections for a range of supercritical