This paper is devoted to the linear dynamics of liquid-structure interactions for an elastic structure filled with compressible liquid (acoustic liquid), with sloshing and with capillarity effects on the free surface in presence of a gravity field. The objective is to detail the formulation and to quantify the role played by the elasticity in the neighborhood of the triple contact line between the free surface of the compressible liquid and the elastic structure in presence of sloshing and capillarity effects. Most of the works consider that the structure is totally not deformable (rigid tank). Nevertheless, for taking into account the elasticity of the tank, some works have introduced an approximation, which consists in considering a locally undeformable structure in the neighborhood of the triple contact line. The theory presented requires the use of quadratic finite elements for discretizing a new introduced boundary condition. An application has specifically been constructed and presented for quantifying the role played by the elasticity of the structure in the neighborhood of the triple contact line.