Prefabricated bondable flexible polymer material in thin sheet, slab, or panel form for making tensioned structures such as false ceilings in particular, said mono- or multilayer material such as plasticized PVC, for example, carrying a direct ink jet or silkscreen print of at least one design of shapes and dimensions that are predetermined once the material is under tension; making a tensioned structure such as a tensioned false ceiling, in particular, from such a material, by means of a first step of selecting the type, dimensions, and dispositions of the mono- or polychromatic designs to be printed, said designs being digitized and recorded in a computer memory of a system for controlling a printing machine, printing optionally being performed on a plurality of bonded-together strips of material, and in particular over zones of edge-to-edge bonding between the strips, said printing taking place before or after bonding.