Abstract: The theory model which studied the interaction between optical activity and elastic-optical effect of crystal quartz in the differential laser gyro was presented. The solving method and steps of the model were proposed. Firstly, the stress-induced transformation matrix between the new and old principal coordinate systems, inverse dielectric tensor and gyrotropic dielectric tensor in the new principal coordinate system were calculated. Then applying the transformation matrix between the new principal coordinate system and laboratory coordinate system, the inverse dielectric tensor and gyrotropic dielectric tensor in the laboratory coordinate system was obtained. According to the normal mode equation and material equation, the stress-induced normal modes and corresponding refractive index along the direction of wave vector were analyzed. Through the calculation example, the change of latent model's ellipticity and refractive index as the function of stress for different directions of wave vector was investigated in detail. This model offers a means to analyze the mechanism of production of differential laser gyro's thermal bias, which had some degree of guiding significance in installation of quartz crystal.