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The purpose of this research is introducing a mathematical model for investigating the structural dynamic stability of a three stages launch vehicle. The intended aim of this research is to reveal the effect of concentrate masses on dynamic stability of launch vehicle under a constant thrust. The launch vehicle is modeled as a free-free Timoshenko beam with variable moment of inertia and module of elasticity for each stage. Dynamic stability study with respect to: 1- the magnitude of rotary inertia and shear deformation parameters of the beam; 2- the magnitude of constant follower force. Both divergence and flutter can occur over the range of free-free Timoshenko model.