During a seismic event, fluid storage tanks are subject to sloshing phenomena; their effect on the structural components of the tanks is one of the main aspects to be considered during the design. The movement in successive modal forms of the roof-fluid system determined by the earthquake can cause severe damage to both the containment shell and the floating roof. The fluid-structure interaction imposes extremely complex out-of-plane deformation fields, mainly in the presence of floating roofs with lower flexible resistance. Such deformations can cause severe structural damage and subsequent catastrophic events such as those experienced in the past in Japan and Turkey. In fact, recently recorded earthquakes in Japan and Turkey, characterized by oscillation periods between 3 and 8 sec (long-period ground motion), compatible with the natural first and second slosh frequencies of the fluid-structure system, led to conspicuous problems of instability failure with the consequent sinking of the floating roof. These events dictated a new starting point for the research into the seismic behaviour of roof-fluid-tank systems.