Damage-free　cutting　of　inorganic　non-metal　materials　with　hard　and　brittle　properties,　such　as　Al2O3　ceramics　and　glass,　by　Slab　CO2　laser　was　studied.　The　characteristics　of　cutting　edges　and　cracks　of　the　materials　with　different　thickness　were　investigated.　Based　on　the　optimum　process　parameters,　a　novel　non-coaxial　locating　device　and　a　novel　cutting　method　created　by　the　analysis　on　the　energy　input　and　heating　accumulation　of　laser　cutting　of　thick　materials,　the　damage-free　cutting　with　arbitrary　path　of　these　materials　was　achieved.