This paper deals with the nonlinear finite element computation of the prestressed state of structures partially filled with an incompressible inviscid liquid. The fluid is modeled by hydrostatic follower forces such that no volumetric fluid mesh is needed. Large deformations are taken into account and lead to the fluid height variation of the wetted surface to satisfy the fluid volume conservation. The main originality of this work lies on the use of a level-set approach to handle numerical integration on the fluid–structure interface. The method is developed on 3D problems considering a finite element quadratic mesh. Various numerical examples are computed using a Newton–Raphson algorithm and a quadratic convergence rate is reached by using consistent tangent stiffness operators.