A method and an automated system for calculating structural elements for vibration strength have been developed. The calculation algorithms are based on a new method of forming Rayleigh-type functionals and minimizing them by the coordinate descent method. The use of the coordinate descent method avoids the problems associated with the formation, storage and operation of global matrices of stiffness and mass. This makes it possible to solve large-scale problems using only the operational memory of the PC. The developed approach allows to solve problems on own and forced fluctuations. The software is formed on a modular basis, which allows you to improve and expand this package of applications. The software has been tested on a large number of test and application tasks. The proposed calculation method and the developed automated system were implemented in engineering practice.