This article describes the second order closure progress that was made to calculate compressible homogeneous shear flow with significant compressibility. Several DNS results show that compressibility has an important effect on the pressure-strain correlation. The term recognized as the principal responsible for the change in the magnitude of Reynolds-stress anisotropies. Thus, the pressure-strain incompressible models do not correctly predict compressible turbulence at high-speed shear flow. A method of including compressibility effects in the pressure-strain correlation is the subject of the present study. The concept of the growth rate of turbulent kinetic energy can be used to construct a compressible correction to the Launder, Reece and Rodi model for the pressure-strain correlation. This correction concerns essentially the C ₁,C ₃ and C ₄ coefficients which become in a compressible turbulence situation a function of the turbulent Mach number. The application of the new model shows good agreement with DNS results of Sarkar for cases A ₁, A ₂ and A ₃. These cases correspond to a moderate mean shear rate, so that nonlinear effects are important.