Square and circular coils are two typical topologies for coupling coils and are applied to wireless charging. However, most of the research on coupling coils is based on the finite element model (FEM), which is a time-consuming process for 3-D structure coils. In this paper, on the basis of Fourier⁻Bessel transformation and Dual Fourier transformation, two theoretical models of square and circular coils between two multilayer media are proposed. With the proposed models, we consider several important parameters such as the size of the coils, thickness, and permeability of each layer. Thus, both the self-inductance and mutual inductance of two planar coils can be calculated without much computational time. Additionally, these theoretical models can help designers figure out the different trends of self-inductance and mutual inductance, which has plenty of benefits for the preliminary pad design. Lastly, a prototype with a size of 600 mm × 600 mm and a 200 mm air gap was built in order to verify the proposed models.