Flexible behaviors in new aerospace structures can lead to a degradation of their control and guidance system and undesired performance. The objectives of the current work are to analyze the vibration resulting from the propulsion force on a Single Stage to Orbit (SSTO) launch vehicle (LV). This is modeled as a follower force on a free-free Euler-Bernoulli beam consisting of two concentrated masses at the two free ends. Once the effects on the oscillation of the actuators are studied, a solution to reduce these oscillations will also be developed. To pursue this goal, the stability of the beam model is studied using Ritz method. It is determined that the transverse and rotary inertia of the concentrated masses cause a change in the critical follower force. A new dynamic model and an adaptive control system for an SSTO LV have been developed that allow the aerospace structure to run on its maximum bearable propulsion force with the optimum effects on the oscillation of its actuators. Simulation results show that such a control model provides an effective way to reduce the undesirable oscillations of the actuators.