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Nowadays, wireless power transfer (WPT) gradually prevails and many researchers have devoted themselves to it because it is a safe, convenient and reliable way for recharging electric vehicles comparing to the conventional plug-in contact-based methods. Square coils are commonly used in WPT systems. However, there is few theoretical analysis of self- and mutual inductance of square coils between two magnetic shielding materials. In this paper, in order to study the spatial magnetic field distribution, the analytical model of n-turn square planar spiral coils between two semi-infinite multilayer media is developed based on the Maxwell equations and the Dual Fourier transformation. And then, by means of surface integrals, the self- and mutual inductance can be carried out, with respect to the main parameters of the WPT systems such as the operating frequency, the geometry feature of the coupling coils and the properties of the multilayer media.