This report results from a contract tasking Moscow Institute of Physics and Technology as follows. To predict boundary-layer transition in a rational way and capture its sensitivity to freestream noise, turbulence, surface roughness. steps/gaps/waviness. etc. a toolbox combining receptivity theory with nonlinear Parabolized Stability Equations and Direct Navier-Stokes Simulation is needed. This project addresses this need with theoretical modeling of high speed boundary-layer receptivity to acoustic disturbances as they interact with 3D roughness elements and waviness. The effort is basic. theoretical research on receptivity. Using the multiple-modes method, a compact and computationally robust algorithm providing fast calculations of receptivity characteristics will be developed. This algorithm will be integrated into a computational module that can be linked with a standard stability solver. Receptivity calculations will be made for the conditions relevant to future experiments in the new high Reynolds-number. Mach-6. quiet Ludwieg' tube of Purdue University. This will help to formulate recommendations for design of receptivity experiments and interpretation of the data. The results of the project can also be applied at the component level to assess laminar flow control concepts.