Abstract: A support system is provided for a tank for the storage of fluid media under pressure which tank has its top, bottom and side walls each made up of a series of parallel outwardly convex lobes. The bottom supports of the support system comprise A-frame cradles that are secured to external structure, and have traylike saddles at their apices in which rest blocks of load-bearing heat-insulating material shaped at their tops to fit into interlobe nodal recesses of the tank bottom. When each heat-insulating block is in correct positional relationship with the respective tank bottom recess, the tray in which it rests is filled with synthetic plastics material which sets to anchor the block in place. The support system also comprises top and bottom locating keys which likewise are located at interlobe nodes of the tank top and bottom walls, each consisting of an extension piece or tongue projecting from an interlobe node to engage external support structure.