The causes for the stress birefringence in the undoped Yttrium Aluminum Garnet ( YAG) crystal grown by the Czochralski method were analyzed. On the basis of the theory of facet growth ,the temperature gradient and procedure parameters during the course of crystal growth were adjusted correspondingly ,by way of which ,together with the suitable anneal procedure ,the stress birefringence was reduced remarkably in the undoped YAG crystal.