In the present paper the relaxation properties of uniaxially oriented polymer threads are investigated. Vibrational relaxation in mechanical system with one degree of freedom is analyzed. This system consists of a heavy weight suspended on a light thread made of a uniaxially oriented polymer material. The authors experimentally confirmed the existence of beats for a number of polymer materials (polycapromide, SVM, Terlon, Armos, etc.) at a certain static load level below the glass transition temperature. A physical explanation is given for the existence of the second vibration mode. On the one hand, elastic oscillations occur in the system, on the other hand, according to the barrier model, oscillations of the occupation numbers of energy levels take place. Thus, another vibration mode arises, associated with highly elastic deformation, since highly elastic deformation is determined by the occupation numbers of the corresponding states. At close frequencies the beat effect is observed.