Abstract Towards the development of simplified analysis methods for the vibrational power in built-up plate structures, a circular can upon an infinite recipient plate is considered. The primary aspect considered is the role of the moments at the upper and lower interfaces, with respect to both the input and transmitted power. Where the thickness of the cans top-plate is at least twice that of the side-wall, the moments are shown to have limited influence and, within “engineering accuracy”, it is suggested they can be ignored in an analysis. This greatly simplifies the modelling of the system. Moreover, it is also shown that where the side-walls are thick compared to the top-plate and, accordingly, the rotational stiffness at the upper interface high, the influence of the moments can, and most simply, be accounted for by merely imposing a guided boundary condition upon the top-plate. A substantial simplification results for the modelling of the system and the analysis. Further, it is found that for typical dimensions, there is an extended frequency range over which the response of the side-walls is either mass or stiffness controlled. Thence, it follows that the input and transfer mobilities of the side-walls are comparable to each other, leading to further reduction of the models.