This paper provides a detailed overview of ship structure and propulsion system vibrations, with a particular focus on the excitations caused by the operation of the propeller. Additionally, the paper covers basic concepts and mathematical expressions in the field of vibrations to facilitate a better understanding of the topics discussed. Based on these theoretical considerations and with the use of Femap software package, which is based on the finite element method, a modal analysis was conducted on the ship local structure in the immediate vicinity of the propeller. Modeling of the local structure was based on the analysis of simplified models, where the effects of element size, type of elements, simplifications, additional water mass, and boundary conditions were examined. By reviewing different types of analyses, the most suitable one was selected, and the case of the local structure with and without the additional water mass was considered, during which the occurrence of false modes was observed, and a method for their detection was proposed. Based on the available technical documentation, operating parameters of the propulsion system, and the characteristics of the ship's propeller, the resonant natural frequencies and the corresponding vibration modes were determined. It was found that certain parts of the deck and bulkheads lack sufficient stiffness, leading to a proposed structural modification. The work was carried out in collaboration with Lürssen Design Center Kvarner d.o.o.