The nonlinear dynamics of acoustic instability in supersonic non-equilibrium flows of vibrationally excited gases is considered. We use a numerical model based on the MUSCL algorithm to study the features of the acoustic instability evolution in supersonic non-equilibrium gas flows. The role of chemical composition, viscosity, thermal conductivity, heating and cooling is revealed. The computer model has high spatial resolution, second order accuracy, and allows one to consider different vibrational relaxation times. Two nonlinear wave packets are formed in a supersonic flow of acoustically active gas. These wave structures propagate both against and along the flow, turning into quasi-stationary systems of shock waves or shock wave pulses at the nonlinear stage of development of acoustic instability. The influence of supersonic flow velocity (Mach number) on the nonlinear stage of acoustic instability in non-equilibrium vibrationally excited gases H2, O2 and CO2 is discussed in application to jet propulsion systems and supersonic flow around aerodynamic surfaces.