Receptivity of a high-speed boundary layer on a flat plate to acoustic disturbances is investigated using a combined numerical and asymptotic approach. The leading-edge receptivity problem is discussed with emphasis on physical mechanisms associated with scattering and diffraction of acoustic waves. Analytical solutions provide insight into the interplay of these mechanisms as a function of the angle of incidence of external acoustic waves. The theoretical predictions are in good agreement with the wind-tunnel experimental data of Maslov et al. obtained at free-stream Mach number 6. The leading-edge receptivity model is incorporated into the multiple-modes method to account for the inter-modal exchange downstream from the leading edge. This combined modelling resembles basic features of the direct numerical simulation of Ma & Zhong. A comparative analysis of the leading-edge receptivity and the inter-modal exchange associated with non-parallel effects is presented. The theory allows fast evaluation of the receptivity coefficients and clarifies the physics of the receptivity process. The theoretical results may guide further direct numerical simulations and experimental studies of boundary layer receptivity at supersonic and hypersonic speeds.