3D finite element analysis of thermo-elasitc problem was performed to relate between the crack front geometry and the crack growing velocity in a thermal stress cleaving. In a stable crack growth, the crack front geometry through a plate thickness becomes so as for stress intensity factor to distribute as much same value along a crack front. The faster a crack growing velocity, the wider a crack front leaves from a center of heat source to show stronger stress singularity. Analyzed result explains well the experiments.