Currently, the ferrite plates are widely utilized in couplers of wireless power transfer systems in electric vehicles. In this paper, the nonlinearity of the self-inductance and mutual inductance for the couplers with ferrite plates is intensively studied by numerical calculation method，and four key parameters including the thickness of the ferrite plates，the spacing between the coils and the ferrite plates, the size of ferrite plates and transfer distance are considered. It is found that the nonlinearity of self-inductance and mutual inductance is greatly affected by the thickness of the ferrite plates，followed by the spacing between the coils and the ferrite plates and the size of the ferrite plates，and little affected by the transfer distance. In addition, the saturation current corresponding to the nonlinearity of the self-inductance and mutual inductance is positively correlated with the thickness of the ferrite plates and the spacing between the coils and the ferrite plates，and negatively correlated with the size of the ferrite plates. The saturation current corresponding to the nonlinearity of the mutual inductance increases slightly with the increase of transfer distance. Then, the combination of the four parameters corresponding to the minimum saturation current is provided, and the minimum saturation current is 160 A. That is, when the coil current is less than 160 A，the self- inductance and mutual inductance of the coupler are linear, and the coupler can be treated as a linear device. Finally，the correctness of the simulation is verified by experiment. The linear characteristics of the coupler are used to analyze the magnetic field around the coupler when the current is not large.