This paper deals with a computational methodology for analyzing a fluid-structure system taking into account sloshing and capillarity phenomena. The fluid is assumed to be linear acoustic and the structure is assumed to undergo large displacements/deformations, which induce geometrical nonlinearities in the fluid-structure system. An adapted nonlinear reduced-order model is constructed using a modal characterization of each part of the coupled system. A numerical application is considered in order to study the effects of the geometrical nonlinearities on the dynamical forced response of the structural acoustic system.