This study proposes a novel computational method, employing the integral dynamics of multibody systems to simulate the transverse vibrations of the rotor in a cantilever-type centrifugal pump. This method was applied to the kinematic assembly of the rotor and its supports, with the latter modeled as springs possessing stiffness and damping properties equivalent to those of real bearings supporting the shaft in an actual design. To investigate transverse vibrations within the system, three key observation points were defined—at the locations of the left and right bearings, as well as at the rotor’s center of mass—to allow for a thorough dynamic analysis. Additionally, the influence of motor rotational speed and the impeller’s eccentricity on the transverse vibrations of the supports and the shaft was examined. The results have revealed that transverse vibrations significantly affect the system’s dynamics at lower rotational speeds, leading to the classification of the shaft as flexible. As the rotational speed increases, the system exhibits enhanced dynamic stability. Furthermore, it was found that for impellers with a diameter less than 300 mm, the unbalanced forces are negligible and can be disregarded in pump design. To reduce vibration levels, an elastic damping ring was selected and incorporated into the system. This novel method provides an effective tool for analyzing the transverse vibrations of centrifugal pump rotors and for optimizing vibration mitigation strategies.