exposed to the action of friction and contact forces, the forces of inertia from a washing fluid, etc. The listed phenomena exert a negative impact on the elements of a drill string, bits, downhole motors, and in general lead to a loss of energy and reduce the techno-economic indicators of drilling [1-4]. To refine the parameters of loading and the stressed-deformed state of a drill string, it is necessary to have a well-defined procedure for determining the moments of inertia of its curved sections. Therefore, it is a relevant task for the theory of dynamic stability of elastic systems to investigate the inertial properties of a curvilinear string of pipes at rotation. The solution to this problem is necessary in order to properly conduct a dynamic analysis of drill strings at rotor and rotor-turbine drilling techniques.