Abstarct: Galloping of cables is a kind of self-excited vibration and characterized with high amplitude and low frequency. When ice, modify the cable circular cross section and causes an aerodynamically unstable profile, Galloping occurs. In this research for investigating the nonlinear galloping of cables, considering flexural and torsional stiffness, a cable-beam model is used. In this research two different boundary conditions are considered for cable. The first is a horizontal cable with simply supports, and the second is an inclined cable with one simply support and another is subjected to a sinusoidal type of motion with known amplitude, both of them are formulated with the iced cross section. Assuming low sag to span ratio and using physical parameter values of the cable, the governing equation of motion is obtained as a classical equations of the perfectly flexible cable, plus a further equation governing the twist motion. These two degrees of freedom system is discretized via the Galerkin method, by taking one in-plane and one out-of-plane modes as trial function. Two resulting non-homogeneous ordinary differential equations are coupled and contain quadratic and cubic nonlinearities in both velocity and displacement terms. By using Multiple Scale method in Perturbation for 1:1 internal resonance for simply support cable and 1:1 internal, external and parametric Resonance for cable with support motion, first order amplitude-phase modulation equations, governing the slow dynamic of the cable, are obtained. In this paper the wind speed and the eccentricity of the iced section are set as control parameters. Without consideration the eccentricity, the value of amplitude is increased as the wind speed is increase. But considering the eccentricity reduced to firstly increasing and then decreasing the amplitude.