We study flexural vibrations of a thin rectangular cross section cantilever beam submerged in a quiescent viscous fluid. The cantilever is subject to base excitation and undergoes oscillations whose amplitude is comparable with its width. The structure is modeled as an Euler-Bernoulli beam and the fluid-structure interaction is captured through a nonlinear complex-valued hydrodynamic function which accounts for added mass and fluid damping. Results from a parametric 2D computational fluid dynamics analysis of an oscillating rigid lamina, representative of a generic beam cross section, are used to establish the dependence of the hydrodynamic function on the governing flow parameters. It is found that, as the frequency and amplitude of the vibration increase, vortex shedding and convection phenomena are enhanced, thus promoting nonlinear hydrody-namic damping. We derive a computationally efficient reduced order modal model for beam oscillations incorporating the nonlinear hydrodynamic function and we validate theoretical results against experiments on underwater vibrations flexible beams.