Designing a claw-pole synchronous machine implies solving many 3D nonlinear magnetostatic problems which makes the computation (CPU) time very long. In our model, the mesh is refined to reach the desired level of precision on global quantities such as torque. Since the airgap is very thin (around 0.3 mm for a 100 mm diameter) and a Newton Raphson algorithm requires several iterations to converge, CPU time may be too high. Nowadays, many researches are ongoing to reduce the CPU time, while preserving an acceptable accuracy. One of the most efficient methods is permeance networks but this method is not suitable for complex geometries. Our main contribution is to use a permeance network in the areas where flux lines are easy to guess and to solve a 3D FEM problem in complex geometry areas of the magnetic device: the claw poles and the air gap for example. Moreover, current sources belong to the permeance network model, so that there are no current sources in the 3D FEM problem. Then, a 3D scalar magnetic potential formulation can be used easily. The two classical magnetostatic formulations (magnetic scalar potential formulation (Um – hs) and vector potential formulation (a – j)) are presented in this paper. Then, the hybridization of 3D FEM formulation and the permeance network, is presented. Numerical results are compared with experimental measurements and a good agreement is obtained while reducing the CPU time. Index Terms—Claw-pole synchronous machine, 3D FEM, permeance networks, hybrid models.