Machining of Nomex honeycomb composite (NHC) structures is of critical importance in manufacturing parts to the specifications required in the aerospace industry. However, the special characteristics of the Nomex honeycomb structure, including its composite nature and complex geometry, require a specific machining approach to avoid cutting defects and ensure optimal surface quality. To overcome this problem, this research suggests the adoption of RUM technology, which involves the application of ultrasonic vibrations following the axis of revolution of the UCK cutting tool. To achieve this objective, a three-dimensional finite element numerical model of Nomex honeycomb structure machining is developed with the Abaqus/Explicit software, 2017 version. Based on this model, this research examines the impact of vibration amplitude on the machinability of this kind of structure, including cutting force components, stress and strain distribution, and surface quality as well as the size of the chips. In conclusion, the results highlight that the use of ultrasonic vibrations results in an important reduction in the components of the cutting force by up to 42%, improves the quality of the surface, and decreases the size of the chips.