The accuracy of the beam profile measurements achievable by the current wire scanners at CERN is limited by the vibrations of their mechanical parts. In particular, the vibrations of the carbon wire represent the major source of wire position uncertainty which limits the beam profile measurement accuracy. In the coming years, due to the Large Hadron Collider (LHC) luminosity upgrade, a wire traveling speed up to 20¿m s-1 and a position measurement accuracy of the order of 1¿µm will be required. A new wire scanner design based on the understanding of the wire vibration origin is therefore needed. We present the models developed to understand the main causes of the wire vibrations observed in an existing wire scanner. The development and tuning of those models are based on measurements and tests performed on that CERN proton synchrotron (PS) scanner. The final model for the (wire¿+¿fork) system has six degrees-of-freedom (DOF). The wire equations contain three different excitation terms: inertia forces associated with the fork rotation, parametric terms associated with the fork tips approaching/separating motion, and terms associated with the wire stiffness (Duffing terms). Though forced, parametric, and Duffing oscillators have been treated in the literature, it is the first time that a model containing all those terms is treated through a purely analytical model. The model has been run for different rotation patterns, and the results show the same trends as the measurements. From the simulations, we conclude that fork flexibility is the main cause of the wire vibration.