Abstract: A set of governing equations of non-linear free transverse in-plane vibration of an inclined cable is presented according to the vibration characteristics of small sag cable. The equations reflect the effects of the cable's Irvine parameter and vibration modes on its natural frequencies, and internal non-linear couplings between the cable modes. When single mode vibration occurs, the governing equations are simplified as a classical Duffing equation with a quadratic term. The averaging method is used to solve approximately the Duffing equation. As an example, dynamic responses of a practical inclined cable are analyzed. The results are verified by numerical results.