A linear transformational model of the dynamic deformation of a plane rod is constructed. The end sections of the plane rod are restrained on two-sided sliding supports of finite length, excluding the displacements of the surface points of end sections in the transverse direction. To describe the deformation process of restrained sections of the rod, the S.P. Timoshenko?s shear model is used. For unfixed part the classical Kirchhoff – Love model is used. The conditions for the kinematic coupling of the restrained and free sections of the rod are formulated. Based on the Hamilton – Ostrogradsky variational principle, the equations of motion, the corresponding boundary conditions, as well as the force conditions for the coupling of the sections are obtained in a geometrically linear approximation. Based on the obtained equations of motion, exact analytical solutions of free and forced harmonic oscillations problem of the plane rod were constructed. It is shown that within the framework of the deformation models used, the problems of longitudinal and bending vibrations of the rod are separated. Of these, bending vibrations occurring in a relatively low frequency range are of greatest practical interest. For them, numerical experiments were carried out to determine the three lower natural modes and frequencies of vibrations, as well as the dynamic response during resonant vibrations of a plane rod on the marked frequencies made of a unidirectional fiber composite based on ELUR-P carbon fiber and XT-118 epoxy. A significant transformation of transverse tangential stresses is shown during the transition through the boundaries from the free section of the rod to restrained one. Such transformation due to the difference in deformation models of the marked areas, as well as their pronounced localization in the areas of restrained areas located near the marked boundaries.