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(Received 19 September 1979; accepted for publication 12 October 1979) A three-dimensional heat transfer model for laser material processing with a moving Gaussian heat source is developed using finite difference numerical techniques. In order to develop the model, the process is physically defined as follows: A laser beam, having a defined power distribution, strikes the surface of an opaque substrate of infinite length but finite width and depth moving with a uniform velocity in the positive x direction (along the length). The incident radiation is partly reflected and partly absorbed according to the value of the reflectivity. The reflectivity is considered to be zero at any surface point where the temperature exceeds the boiling point. This is because a ’’keyhole’’ is considered to have formed which will act as a black body. Some of the absorbed energy is lost by reradiation and convection from both the upper and lower surfaces while the rest is conducted into the substrate. That part of the incident radiant power which falls on a keyhole is considered to pass into the keyhole losing some power by absorption and reflection from the plasma within the keyhole as described by a Beer Lambert absorption coefficient. Matrix points within the keyhole are considered as part of the solid conduction network, but operating at fictitiously high temperatures. The convective heat transfer coefficient is enhanced to allow for a concentric gas jet on the upper surface as used for shielding in welding and surface treatment, but not cutting. The system is considered to be in a quasi-steady-state condition in that the thermal profile is considered steady relative to the position of the laser beam. The advantages of this method of calculation over others are discussed together with comparisons between the model predictions and experiments in laser welding, laser arc augmented welding, laser surface treatment, and laser glazing. The system is assumed to be in a quasi-steady-state condition after the keyhole initiation period which for most practical purposes may be considered instantaneous.