A mechanical breaking process after laser scribing is indispensable to complete the separation of glass substrate since the crack depth induced by the laser scribing is limited. Laser irradiation along the laser scribed line is introduced in this paper as a crack propagation method in depth direction after the laser scribing of a relatively thick glass in order to make the mechanical breaking easier. Since the separating load decreases by propagating the scribed crack deeply, it contributes to the inhibition of glass particle generation. The target of this research is to clarify the mechanism of crack propagation by the laser irradiation along the laser scribed line. Two-dimensional thermal elasticity analysis was conducted by a finite element method based on the experimental results in order to theoretically estimate the laser irradiation condition, which propagates crack. The following results were obtained. Compressive stress is generated on the glass surface and tensile stress is generated inside the glass by the laser irradiation along the laser scribed line. The tensile stress concentrates at the crack tip induced by the laser scribing, and the crack propagates into the depth direction. The condition of crack propagation can be estimated from the maximum surface temperature and the maximum tensile stress of the crack tip in practical processing velocity (200 mm/s or more mm/s).