Abstract: Aerial remote sensor is very important for obtaining ground information. For high-mach flight condition, the mathematical model of optical window is the foundation for developing research on remote imaging. The shape and refractive index distribution of optical window are affected by high-mach flight condition, so that the image quality of remote sensor would also be affected. It is necessary to establish mathematical model of optical window in order to improve image quality. Firstly, optical window under high-mach flying condition was described and input parameters and boundary conditions of analysis were defined. Secondly, the temperature field model and deformation model of optical window were established. Then, the characteristics of refractive index was presented as a function of temperature. Finally, the mathematical model of optical window under the condition of high-mach flight was derived.