Abstract: A self-tensioning hold down apparatus functions to secure an object to a support rack, for example a bicycle to a bicycle support rack. The apparatus has a catch that exerts a variable force downward on the bicycle that holds the bicycle down on the support rack and compensates for movement of the bicycle on the support rack due to vibration and compensates for any loss of air pressure in the bicycle wheels and thereby prevents the bicycle from falling from the support rack. In a variant embodiment the apparatus has a pair of cradles that exert a variable force upward on the bicycle that holds the bicycle between the cradles and the catch.