Effect of altitude is discussed in the unsteady separation of multi stage rockets. Axisymmetric, unsteady and turbulent Navier stokes equations are solved numerically. The governing equations are split into a hyperbolic inviscid part and a parabolic diffusion part. The hyperbolic part is solved by an explicit second-order time and space of Godunov-type scheme. Moving mesh and moving boundary algorithm are used in the numerical simulation. Separation of missile staging is simulated at 10, 20, 30 and 40 kilometers altitudes, and 10 Mach number. The flow physics of injection of a secondary supersonic jet into a hypersonic turbulent primary core over a missile configuration is studied numerically. The injection occurs opposite to the free-stream direction. It is shown that the intense interactions between the jet flow and the main free-stream have a noticeable effect on the aerodynamic loads. High momentum of the jet injected to the main flow of rocket causes interaction of shock waves and consequently it changes flow pattern. The aerodynamic forces can be changed significantly by the intense jet flow interactions. The results show that drag forces of head and body of the rocket are irregularly periodical. Amplitude of drag force has been increased by altitude. At primary time of separation, rate of displacement of head and body has incredible behavior in various altitudes too.