ESDU 92008 describes the features of a viscous-coupled calculation method that are required to predict transonic flow over an aerofoil with some boundary layer separation. One particular method is considered in detail, its technical features are detailed, and the input and output are described together with the computer requirements. Its performance is compared with selected wind-tunnel data on pressure distribution, shock strength and location, trailing-edge pressure, and a separation boundary associated with trailing-edge pressure divergence together with the drag coefficient near that condition. The separation boundary was predicted to within about 0.08 in lift coefficient and the drag coefficient within 10 per cent. Some details and trends were dealt with less satisfactorily; in particular, the often observed gradual increase in trailing-edge pressure prior to its rapid fall as separation becomes more extensive was not predicted and it seemed the extent and effects of shock-induced separation were underestimated.