Accurate modelling is necessary for designing a wireless power transfer (WPT) system and currently, first harmonic approximation (FHA) is widely used. However, it is not accurate for WPT systems with a strong coupling, such as fast charging of electric vehicles with a coupling coefficient of 0.80, compared to the conventional wireless charging with a coupling coefficient of 0.15–0.30. This study develops accurate models for WPT systems with series–series (SS) and LCC–LCC compensations. For the SS compensation with a strong coupling, the transmitter and receiver currents are distorted, leading to much larger values than the estimations from FHA, which determines the selection of power switches and resonant capacitors. For the LCC–LCC compensation, the transmission coil currents are only highly distorted with rich third-order harmonics at the vicinity of the 0.889 coupling coefficient, leading to low efficiency and large coil current ratings. For the experimental prototype, the efficiency drop can be over 3%, which is significant, especially for high-power systems. The WPT system with the LCC–LCC compensation should avoid operation in the vicinity of this particular coupling coefficient. Furthermore, experiments are conducted, and the results perfectly match the calculations, demonstrating the accuracy of the proposed models.