The fundamental physical phenomena occurring during the process of laser cutting are still only slightly understood, and thus the need to develop mathematical and numerical models to optimize the process parameters has become unavoidable for obtaining products with superior quality and for better use. It is in this context that we propose a new approach by building a model to study the laser cutting process, by including several physical mechanisms which interact during the cutting process, such as the laser-metal interaction (wavelength effect, energy absorption, …), the phase change (solidification/fusion), the heat transfers, the fluid flows with influence of the free surface, the turbulent gas jets, and the kerf formation. In view of the complexity of the phenomena put into action, the fundamental mechanisms related to the cutting process are very difficult to understand and then to model. It is indeed necessary to take into account all of the aforementioned interactions, avoiding excessive simplifications and simulation loss of accuracy. The models found in the literature are often simplified and focus on effects such as assisting gas contribution used to evacuate the molten metal film, considered as forces applied to the gas-material interface, which is likely to neutralize given interactions. In these conditions, after highlighting most of the interactions that are involved, we provide a generalized model which accounts for laser absorption, phase transition, heat transfer, fluid flow, kerf formation, and assisting gas jet flow. In other works, each of these contributions has been considered separately, while in this paper, we make an attempt to combine all of them within a single general model that is likely to account for the physical reality of the laser cutting process.