We propose to use a unified mathematical model of deformation of thin-walled structures made from laminated composite materials for problems of stability and free vibrations of preliminary stressed structures. In order to study stability, a dynamical method based on the analysis of oscillations of system nearby to its equilibrium state is applied. A unique numerical algorithm, which was described in detail earlier by the authors, is proposed for efficient solution of the problems of statics, dynamics, and stability. The results of analysis of free vibrations and stability of the heads of missiles are presented.