This paper describes a two-dimensional analytical model to predict the magnetic field distribution in axial-field magnetic gears by using the sub-domain method. The sub-domain method consists in solving the partial differential equations linked to the Maxwell's equations in each rectangular region (magnets, air-gaps and slots) by the separation of variables method. The proposed model is based on a two-dimensional approximation for the magnetic field distribution (mean radius model) i.e. the problem is solved in 2D Cartesian coordinates. One of the main contributions of the paper concerns the analytic solution of the magnetic field in a slot open on the two sides (space between the ferromagnetic pole-pieces). Moreover, it is shown that the analytical model and the 3D finite elements simulations follow the same trends in the determination of the optimum values for the geometrical parameters. As the analytical model takes less computational time than 3D numerical model, it can be used as an effective tool for the first step of design optimization.