In this paper, we analyze nonlinear torsional vibrations of thin rectangular cross section cantilever beams undergoing mod-erately large base excitation within a quiescent viscous fluid. The structure is modeled as a linear Euler-Bernoulli beam while the distributed hydrodynamic loading acting on the vibrating structure is described via a nonlinear complex valued hydrody-namic function which incorporates added mass and fluid damp-ing caused by moderately large rotations. Results of a two di-mensional computational fluid dynamics parametric analysis of a pitching rigid lamina, representative of a generic beam cross section, are employed to study the dependence of the hydrody-namic function on the governing flow parameters. We find that, as the frequency and amplitude of the oscillation increase, vor-ticity shedding and convection increase, thus resulting into non-linear hydrodynamic damping. We derive a tractable form for the hydrodynamic function suitable for studying the nonlinear fluid-structure interactions in large amplitude torsional underwater vibrations. We establish a reduced order nonlinear modal model based on these findings and we validate theoretical predictions against experimental results on underwater torsional vibrations of flexible cantilevers.