The outstanding tensile strength of some materials are used in compression applications by using air pressure to supply the outward force on an enclosure and by using interior tension members to maintain the geometry of the air-pressurized structure. The air pressure on each face of the structure is balanced by the tension in the tension members. Due to the high modulus of the tension members, the air-pressurized structures are very rigid. It is the air pressure that actually supports any load placed on the structure, but it is the tension members that maintain the geometry when the load is removed, and the strength of the tension members determine how much air pressure can be sustained. The mass of tension material required in such a structure is roughly equivalent to the amount of filament material required in a cable to support the same load. The Compressed-air Rigid Building Blocks can be stacked like bricks to form strong, lightweight walls, buildings, towers, and other structures.