Most of the medium-size ships are powered by large-bore, long-stroke, slow-speed and two-stroke diesel engines in order to improve the fuel efficiency. Such a propulsion plant develops low-frequency excitation forces/moments of significant magnitude. A RO/RO car/truck carrier is also one of the cases. In this paper, the rational methods for analysis of vertical and coupled horizontal-torsional vibrations are presented. Taking account of unusual characteristics of the hull form and structural systems, the emphasis is put on modelling methods based on beam analogy, calculation of system parameters such as added mass and its center, polar added-mass moment of inertia, shear coefficient of hull sections and coupling degree in antisymmetric modes, and modal analysis of forced vibrations.