A previously-developed three-dimensional conduction model for scribing of a thick solid has been extended to predict the transient temperature distribution inside a finite thickness slab that is irradiated by a moving laser source, and the cutting rate and profile carved by evaporation of material. The laser may operate in CW or in pulsed mode (with arbitrary temporal intensity distribution) and may have an arbitrary spatial intensity profile. The governing equations are solved, for both constant and variable thermophysical properties, using a finite-difference method on a boundary-fitted coordinate system. Results for cutting rates and profiles, as well as for temperature fields, are presented for materials that ablate or decompose upon laser irradiation (without significant formation of liquid), for different material thicknesses, traverse speeds, pulsing conditions, and power levels. For drilling (zero traverse speed), a numerically much more efficient two-dimensional axisymmetric version of the model has also been implemented, and similar results for drilling behavior are presented as well.