Abstract Non-linear vibrations of an elastic plate in heavy fluid loading conditions are considered. The structural non-linearity is taken into account along with the fluid non-linearity in a full Bernoulli integral formulation for the contact acoustic pressure and with the non-linearity in the formulation of the continuity condition. The modal analysis in spatial co-ordinates is used along with the method of multiple scales to search for a stationary response in the time domain. Resonant frequencies of a fluid-loaded plate are detected in a coupled formulation of structural acoustics and typical excitation conditions (a weak resonant excitation, hard monochromatic sub- and super-harmonic excitations, an excitation by two driving forces) are explored. The roles of the structural non-linearity and the non-linearity in the formulation of the fluid response are compared.