Abstract: The invention provides cryogenic structures, e.g. vessels or tanks joined by longerons, which are made of durable plastic composite materials rather than of metal, which vessels can contain cryogenic materials including fuel, without need of a liner or other weighty layers of the prior art. The structures are made of, e.g. a fiber network impregnated with a matrix of thermoset plastics, thermoplastics or a combination thereof. Thus the invention includes a cryogenic vessel of, e.g. 3 tank lobes, made of a composite of plastic reinforced with fibers, which lobes are joined together and supported by woven, cruciform shaped longerons which are also impregnated with plastic, to define a composite support member.