The cleaving process has the potential to replace the dicing of thin wafers. Its inherent advantages are no mechanical forces to the substrate, no material losses, and high edge quality. In order to determine the fundamental mechanisms leading to a reliable cleaving process the complex interaction of wavelength and temperature dependent absorption, heat transfer, material elongation and finally crack formation is theoretically described and experimentally verified. A successful process observed if sufficient thermal stress can be generated to induce a crack and if no surface deformation occurs due to overheating. Most relevant parameters determining the process window are irradiated power, cutting speed, and focus spot size. The results of these parameter variations are presented. Accuracy and reproducibility is demonstrated by cleaving stripes of different widths fulfilling the requirements of the electronic packaging industry. In the third section the influence of the crystalline orientation is investigated. As a result mono-crystalline silicon exhibits an anisotropic behaviour when changing the cutting direction whereas for polycrystalline substrates a permanent change of the crystal structure is found at the grain boundary. Finally, the obtainable edge quality is presented briefly, which leads to higher sample strengths compared to conventional laser and mechanical processes.