This paper is devoted to a numerical approach in vibroacoustics of a linear elastic structure coupled with a compressible liquid with sloshing and capillarity effects. This work is based on a new formulation for the boundary condition on the contact angle. A reduced-order model is constructed using a projection basis made up of elastic modes, acoustic modes, and sloshing-capillarity modes. Then a numerical study of a coupled fluid-structure system discretized with finite element modeling is presented.