Composite panels each having a casing and insulating material in the casing are mounted in a covering layer over the inside of a supporting structure by mechanical fastening means. Joint cover members including insulating material and outer facing material are disposed in the spaces between casings of adjacent composite panels. The outer facing material is sealed to front panel portions of the casings to form a primary barrier for cryogenic liquids therewith. An additional secondary barrier may be provided by using composite panels with interior panels in the casings sealed to inner sides thereof and dividing the casings into front and rear compartments, each having insulation therein, and using front and rear joint cover members, the outer facing material of the rear joint cover members being sealed to outer sides of the casings of adjacent composite panels to form a secondary barrier with the interior panels of the composite panels.