The process of cutting metals with a laser beam is described by a mathematical model comprising a set of balance equations for mass, momentum and energy. The molten film at the cutting front is defined as the control volume. The calculation yields average values for the characteristic macroscopic state of the cutting front, such as temperature, melt film velocity and melt film thickness. All relevant parameters of the laser beam and of the process gas flow are considered in the model. Numerical evaluations of the analytical model provide explanations of the process behavior both for inert and for oxygen gas cutting. The narrowing of the kerf width with increasing speed is explained by heat conduction. Furthermore, the model shows that the evaporation temperature is reached at high velocities for thin metal sheets. Using a higher gas pressure increases the diffusion limited oxidation rate and provides higher cutting velocities, while the fraction of oxidized metal decreases substantially with increasing speed. ©1996 American Institute of Physics.