The wireless power supply solution has shown great advantages in rail transit applications, such as maglev trains and trams. However, research works on designing the magnetic coupler for wireless charging system in rail applications, which is a crucial problem, are not sufficient. Considering the high power and lightweight requirements, this article selects the coaxial M-shape magnetic coupler with LCL/S compensation for railway applications, which contains the transmitting rail and the receiving coil wound on an M-shape magnetic core. First, analysis was conducted on the requirements for inductance parameters of the magnetic coupler under the circuit constraints, including transmission power, input and output voltages, and component electrical stress, etc. Then, the influence of the geometric parameters of the coil structure and misalignment on its inductance parameters is analyzed. Based on these analysis results, the design method for the M-type magnetic coupler based on the lightweight principal is proposed. The geometric parameters are designed following a certain sequence to minimize the number of iterations and FEM simulation parameter sweeps, making the design procedure suitable for engineering practice. According to the proposed method, the magnetic coupler for a 360 kW wireless charging tram is designed and implemented. Through simulations and experiments, the magnetic coupler is verified to be feasible for the system with light weight. [ABSTRACT FROM AUTHOR]