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. This analytical models can be used to investigate the different characteristics of self- and mutual inductance of square coils with the variation of certain main parameters, which is helpful for optimizing the couplers’ geometries and the magnetic field distribution. To validate the proposed theoretical model, a 600 mm × 600 mm with a nominal 200-mm-gap prototype has been built. At last this prototype is tested with the lateral misalignment.