Stability of a supersonic near-wall flow over a shallow grooved plate in the freestream of Mach 6 is investigated by means of numerical simulations and wind-tunnel experiments. Numerical solutions of two-dimensional Navier-Stokes equations are used to model propagation of artificial disturbances of several fixed frequencies generated by an actuator placed on the wall. It is shown that the high-frequency forcing excites unstable waves in the flat-plate boundary layer. These waves are relevant to the second-mode instability. The wavy wall damps the disturbances in a high-frequency band while it enhances them at lower frequencies. Stability experiments are conducted in the Institute of Theoretical and Applied Mechanics Tranzit-M shock tunnel under natural freestream conditions. The measured disturbance spectra are similar to those predicted numerically. They contain a peak associated with the second-mode instability. This peak is damped by the wavy wall, while a marginal increase of the disturbance amplitude is observed at lower frequencies. Although the experiments qualitatively confirm the wavy-wall stabilization concept, further stability and transition measurements are needed to clarify its robustness. Copyright © 2012 by Andrey V. Novikov. Published by the American Institute of Aeronautics and Astronautics, Inc.