This paper aims to present a non-dimensional analysis which characterizes the structural vibration induced slosh damping for a single-degree-of-freedom (SDOF) tank system under vertical motion. We identify several key non-dimensional relations which are then characterised in terms of slosh loads and dissipated power using volume of fluid (VoF) computational fluid dynamics (CFD) simulations. Scaling-laws are then constructed for future quantification of these phenomena. The fitted scaling rules are shown to offer a clear correlation for the selected SDOF system for liquid density ratio and flow Froude number