Purpose. Conducting research aimed at choosing the rational modes of flashing the tubular billet by stabilizing the dynamic characteristics of the drive power line of heavy-duty piercing mills TPA. Methodology. The dynamics of the power line of the piercing mill of the pipe-rolling unit (TPA) are considered, taking into account the peculiarities of the behavior of the spindle hinges and the mechanism for setting the work rolls. Findings. The differential equation of motion of the line of the main drive of the piercing mill is composed and its numerical solution is given. An adapted three-mass dynamic model of the system is considered and a solution is obtained using the software Solid Works IT Simulation X. The basic conditions for the occurrence of unstable dynamic phenomena in the fieldline and the installation mechanism of the piercing mill rolls are formulated. It is shown that the unstable dynamics of the system are one of the main reasons for the discrepancy between the results of well-known theoretical, experimental studies and pipe thickness measurement at TPA 350 piercing mills. Originality. The main causes of the emergence of parametric oscillations in the drive of the working stand of the piercing mill, the installation mechanism of the work rolls in connection with the mechanism of formation of the thin-wall thickness of pipes are established. The areas of stability of the system’s functioning are determined depending on the operating modes and the angle of feed of the work rolls, taking into account the spatial position of the elements of the spindle device. The necessary and sufficient stability conditions for the joint stable functioning of the power line elements of the piercing mill are formed. Practical value. To stabilize the processes for flashing the tubular billet, a scheme has been proposed for upgrading the spindles of the main drive and the mechanism for installing the work rolls of the piercing mill No. 1 of TPA 350. The results are applicable to similar helical rolling mills. Keywords: firmware, billet, mill, pipe, uneven stroke, varying thickness, dynamics, drive, roll, oscillations, spindle, Cardan, hinge, moment of inertia, rigidity, drum, installation mechanism, stability.