Simulations and identification of non-linear parameters are applied on two models that describe the vibration due to parametric resonance in cables of cables-stayed bridges. The aim of this work is to study the dynamic response predicted by the two models under random excitation, as well as to develop a suitable strategy for system identification from random data. In one model the parametric excitation is treated as an arbitrary displacement introduced in one end of the cable. In the second model, such excitation is coming from an external force acting on the pylon or deck of the bridge to which the cable is coupled. The pylon or deck is modeled as a Single Degree of Freedom System. In both models the cable response is obtained by a simulation method based on digital filters. The studied identification technique is based on random excitation. In this method the non-linearity is modeled as a feedback forcing term acting on an underlying linear system or systems and the parameter estimation is performed in the frequency domain by using conventional MI/SO techniques.