The motion and stresses of a non-Hookian elastic flexible cable in plane motion under tension are described with four simultaneous quasilinear, partial differential equations which are totally hyperbolic. The propagation of the longitudinal elastic waves and the transverse waves are described by the four characteristics. From the characteristic equations, solutions for simple longitudinal waves and simple transverse waves are obtained for uniform Hookian cables. The problem of an infinite string moved at one point with a constant velocity can be solved. Solutions also have been obtained for the interaction of transverse and longitudinal waves with sharp fronts.