This paper describes the implementation and numerical evaluation of a transient 3D computer simulation of the CO2 laser cutting process. Utilizing Crank-Nicolsen-Finite- Difference equations for the solution of the Fourier heat transfer equation with Newtonian convection, the temperature distribution is predicted. For high accuracy the mesh is of non-equidistant nature, following a Weibull Distribution for the grid spacing. A parallel computation solver is used, based on Divide-and-Conquer Gaussian elimination for banded matrices, to calculate the nodal temperatures using a cluster of two HP J5000 workstations. Included in the solution is the behavior of the material during phase change, while the open structure of the developed software allows incorporation of effects such as surface oxidation, radiation and limited convective flow. The main area of interest is the cutting capability with respect to varying material thickness, cutting speed, power of the laser, laser mode, focal spot diameter and material properties, as well as the effect of these parameters on the quality of the cut.