Dynamic stability of a free flight aerospace vehicle is investigated in this paper. Firstly, the slender rocket body is modeled as a classic uniform beam that subjected to constant end rocket thrust. The one-dimensional free-free beam under follower force is established for structural model to discover dynamic stability. Equations of motion of vehicle is derived by applying extended Hamilton's principle for non-conservative systems. Natural frequencies of rocket are determined and critical thrust is obtained by using finite element method. It is noted that, transverse vibrational modes differ by thrust value. Secondly, natural frequencies of non-homogeneous beam are discussed by considering that rocket has different types and number of stages. Numerical results for both cases are represented.