The goal of this research is to develop a theoretical model of a new concept of laser machining, which utilizes two intersecting laser beams, so that optimization of the process parameters will be possible. The importance of this new process will be limited if the material removal rate and the surface quality and integrity of the workpiece are not optimized. The theoretical model will be tested and compared to experimental results. Workpiece materials to be studied are ceramics, composites and hardened steels. This new concept of laser machining is capable of producing three-dimensional shapes similar to those produced by conventional machining, but with increases in energy efficiency of the process by a few orders of magnitude. Potential applications include manufacturing of ceramic engines and composite aircraft.