ESDU 81020 gives a method for predicting the lift coefficient versus Mach number curve defining separation from a series of pressure distribution calculations using computer codes that strictly do not apply to flows approaching separation. From an analysis of wind-tunnel data two separation criteria were developed for use with the calculated pressure distributions, depending on whether separation occurred initially at the upper-surface upstream shock location or just upstream of the trailing-edge. Separation was defined as occurring when the trailing-edge pressure coefficient diverged by 0.05 from an extrapolation of its trend with freestream Mach number or lift coefficient in attached flow. Because conditions for initial separation change along the complete separation boundary both criteria have to be considered. A detailed step-by-step explanation of the method is provided. The method was developed using calculations by the viscous Garabedian and Korn program with a lag entrainment boundary layer theory, but will apply using any comparable method for computing aerofoil pressure distributions. It applies to round-nosed aerofoils with or without camber with sharp or blunt bases. The experimental data used to develop the separation criteria covered a freestream Mach number range from 0.6 to 0.85 for Reynolds number based on chord of 2.5 to 20 million with transition fixed within a few per cent of the leading-edge on both upper and lower surfaces. The method predicts the boundary within 0.03 in lift coefficient where separation lift coefficient varies slowly with Mach number and within 0.005 in Mach number where the separation Mach number varies slowly with lift coefficient.