A method is presented for the stress analysis of flight vehicles under different flight conditions including gust and control surface deflection (or maneuver) using the governing equations of rigid-body motions and elastic deformations. The Lagrangian approach is used to derive the governing equations of motions. For this purpose, the basic equations of motions are derived in terms of potential energy, kinetic energy and generalized forces, which are, in turn, computed in terms of rigid-body motion variables, elastic mode shapes and cla(x) distribution for aerodynamic forces. By replacing them into the relations obtained, the governing equations for aeroelastic behavior of the vehicle are derived. The system of aeroelastic equations of motions is solved in time domain using numerical methods. The stress distribution is determined using the relation between modal variables and strain at each point. Finally, the prepared code is verified through comparison of the results obtained from the proposed method for the stability of a rocket and the same results reported by other studies. Also additional information such as maximum stress in the body is presented for various flight conditions.