A Finite Element approach is presented for the computation of linearized hydroelastic vibrations of partially filled tanks, around a prestressed state. The focus is given on the competition between the prestressed and added-mass effects on the dynamic behavior of the fluid-structure system. First, by taking into account geometric non-linearities, a quasi-static solution of a tank loaded by hydrostatic follower forces is computed [1]. Then, the linearized hydrostatic vibrations around the prestressed configuration are computed with a standard fluid-structure formulation [2, 3]. The methodology is finally applied on a cylinder partially filled with liquid, showing very good agreements between our numerical results and experiments from [4].