Constitutive relationships and elastic specific energy of cylindrical air cushion mats were derived and analyzed on the base of mechanical and physical theories. The investigation of their influencing factors was also carried out. The results show that: the stress-strain curve is observed as an exponentially under radial load and the elastic specific energy increase with the climbing inner pressure, but is affected little by the section area. the elastic specific energy of the material decreases dramatically with the upswing of the inner pressure, but exhibits unobvious at low strain.