A numerical procedure is presented for computing characteristics of Tollmien–Schlichting (T-S) waves in the course of their downstream evolution. It is based on the Global Stability Analysis of steady solutions of the full compressible Navier-Stokes equations and, therefore, does not have the restrictions associated with the parallel or quasi-parallel flow assumptions used in the classical methods of the linear stability analysis based on the boundary layer approximation. Hence, the methodology may be applied not only to simple boundary layers on smooth surfaces but also to non-parallel flows, e.g. those over surfaces with irregularities (steps, gaps, etc.). The developed procedure is validated by the comparison of the computed distribution of the T-S amplification factor (N-factor) in the zero pressure gradient boundary layer with the similar distribution computed based on the solution of the Orr-Sommerfeld equation and is shown to be accurate and robust.