Machining of Nomex® honeycomb materials is the biggest challenge in industry because of the complex forms and geometry of the honeycomb structure. The latter is characterized by a low density with orthotropic mechanical behavior. The thin walls of the composite structure make the shaping of this material very difficult. Studying interactions between the cutting tool and material, cutting forces, and chip formation allow to understand the machining process of Nomex® honeycomb. This paper presents 3D numerical modeling of machining Nomex® honeycomb using different orthotropic approaches and failure criteria: (i) monolayer isotropic approach, (ii) monolayer orthotropic approach with Tsai-Wu failure criteria, and (iii) monolayer orthotropic approach with Hashin failure criteria. A comparison between experiments and numerical cutting forces was performed to validate the proposed model. The interaction between the tool and the honeycomb walls, which make it possible to observe the different stages of the chip formation process, was carefully modeled.