On the basis of the viscid compressible gas model with heat conduction gas-column oscillations excited by a non-equilibrium initial pressure distributions are numerically studied. Transformation of initial continuous pressure sharing in the oscillatory process, accompanying forming the shock waves was analysed. During the calculations the convection and heat diffusion stages of the turning a system to equilibrium state process are considered. As a result undertaking the payments is discover that on the completion of the convection stage (in the absence of gravity power) effect of pressure leveling under non-equilibrium sharing of the density and temperatures of the gas along the pipe is observed. At the deceleration of convection process, transition to equilibrium is realized by means of heat conduction.