A two-degree-of-freedom non-linear elastic model is considered to analyze the effects of non-linearities on the free motion of a suspended cable. The discretized model is obtained by referring to simplified kinematics of the cable; the equations of motion which show quadratic and cubic non-linearities are solved through the multiple time scale perturbation technique. The monofrequent oscillations of the system are studied in order to analyze the modifications of frequency and motion amplitude of the modal oscillations due to geometric non-linearities in the absence of internal resonance. The possibility that effects arise due to non-linear coupling is examined. A numerical analysis is made for the first symmetric mode for different amplitudes of motion by parametrically varying the geometric and mechanical properties of the cable. The correction of frequency for the in-plane oscillation varies appreciably with the cable properties due to prevalence of either the quadratic or cubic term. In the out-of-plane monofrequent oscillation non-linearities establish a coupling between the two components of motion which strongly influences the frequency correction.