The use of a suitable modeling technique for the optimized design of a magnetic gear is essential to simulate its electromagnetic behavior and to predict its satisfactory performance. This paper presents the design optimization of an axial flux magnetic gear (AFMG) using a two-dimensional (2D) magnetic equivalent circuit model (MEC) and a Multi-objective Genetic Algorithm (MOGA). The proposed MEC model is configured as a meshed reluctance network (RN) with permanent magnet magnetomotive force sources. The non-linearity in the ferromagnetic materials is accounted for by the MEC. The MEC model based on reluctance networks (RN) is considered to be a good compromise between accuracy and computational effort. This new model will allow a faster analysis and design for the AFMG. A multi-objective optimization is carried out to achieve an optimal volume-focused design of the AFMG for future practical applications. The performance of the optimized model is then verified by establishing flux density comparisons with finite element simulations. This study shows that with the combination of an MEC-RN model and a GA for its optimization, a satisfactory accuracy can be achieved compared to that of the finite element analysis (FEA), but with only a fraction of the computational time.