Fluid-structure interaction (FSI) significantly influences the dynamic behaviour of submerged or fluid-containing structures. The “added mass” effect lowers natural frequencies and alters mode shapes. Understanding and accurately predicting this phenomenon is crucial for the design and safety assessment of various engineering systems, from offshore structures and storage tanks to hydraulic machinery. This paper presents a detailed numerical procedure, to investigate and quantify the added mass effect on the modal characteristics of a simple cylindrical container. The methodology for setting up the coupled fluid-structure problem, inherently capturing the inertial effects of the contained water, is described. The study validates the numerical approach against experimental results, showing frequency reductions of 24-33% due to added mass, with prediction errors for primary modes below 4%. This work establishes a reliable and validated FEM-based procedure for analysing vibroacoustic phenomena due to added mass, serving as an essential foundation for future analyses of such effects in more complex geometries, such as Francis turbine runners, where precise modal characterization is critical for operational dynamics and resonance avoidance.