It is of great significance to measure the residual stress distribution accurately for optical elements and evaluate its influence on the performance of optical instruments in optical imaging, aviation remote sensing, semiconductor manufacturing, and other fields. The stress of optical elements can be closely related to birefringence based on photoelasticity. Thus, the method of quantifying birefringence to obtain the stress becomes the main method of stress measurement technologies for optical elements. This paper first introduces the basic principle of stress measurement based on photoelasticity. Then, the research progress of stress measurement technologies based on this principle is reviewed, which can be classified into two methods: polarization method and interference method. Meanwhile, the advantages and disadvantages of various stress measurement technologies are analyzed and compared. Finally, the developing trend of stress measurement technologies for optical elements is summarized and prospected.