Compliance must be supplied to any surface mooring to allow the buoy to move with the waves and currents, and remain moored in position. This can be supplied with a traditional chain catenary or newer compliant elastic tether or stretch hose technologies. Some applications of each of these three techniques are shown, with the emphasis placed on the use of compliant elastic tethers. For modeling and designing these moorings, the elastic modulus of the tether material must be known. Therefore, a new and used piece of elastic material was terminated, tested for the stretch-strain relationship under set conditions, and the elastic modulus calculated. For these tests, the elastic tether was stretched out to a mean elongation between 100 and 250%, then cycled about that stretch by 25 and 50% to duplicate a moored application. The resultant elastic modulus is presented to aid in mooring design. At low elongations, the elastic modulus is constant at about 125 PSI, but as the mean elongation increases the modulus increases, and as the cycle tension increase the modulus also increases, reaching a maximum of 900 PSI at 275% stretch.