As the key component of inertial navigation system, the output accuracy of angular velocity of RLG plays a decisive role in the positioning and orientation accuracy of navigation system. When the external environment (such as temperature) changes, the optical path of the RLG will be deformed to a certain extent, which will lead to the offset of the input axis of the RLG, and then lead to the inaccurate angular velocity of the sensitive carrier of the RLG. In this paper, the optical path deformation and the input axis offset of RLG are calculated and analyzed from theoretical calculation and numerical simulation. The simulation results show that there is a positive correlation between the deformation of the optical path and the offset of the input axis. When the light spot on the on the two plane mirrors of the RLG moves by 0.2mm, the cosine value of the offset angle of the input axis of the RLG is about 0.999 96, that is, the angular velocity error is about 0.004%. Under the guidance of theoretical analysis, the experiment is designed. The experimental results show that when the temperature changes greatly, the optical path of some RLGs will deform and the input axis of laser gyroscope will shift. The cosine value of the shift angle is about 0.999 980, that is, the angular velocity error is about 0.002%. This paper provides a reference for establishing the temperature compensation model of RLG.