Crack propagation is induced by thermal stress in the laser cleaving process, which is a prospective technique for dividing the substrates of hard and brittle materials such as glass, ceramics, and some semiconductor materials. Because the control of thermal stress distribution is essential for achievement of high accuracy in the process, various models have been developed for theoretical analyses to predict the stress distribution and estimate the effect of it. Besides, authors have developed a photoelastic observation technique for stress distribution in the laser cleaving process. In the present paper, the authors propose a procedure to compensate the distribution of stress direction within the substrates in order to apply the observation technique for the laser cleaving of single crystalline substrates which exhibit anisotropic photoelasticity. Single crystalline sapphire substrates are used as specimen in experiment to confirm the proposed procedure. Obtained results show the discrepancies between the principal stress direction and the birefringence direction of observation light in plane polariscope. And, the discrepancy depends on the crystal orientation with respect to the vibration plane of polarized light of the polariscope. This result is used to compensate the distribution of principal stress caused within the sapphire substrates during the laser cleaving process.