Dispersion control is one of many key techniques in ultrashort laser pulse generation and its applications. By controlling the optical path of wavelength in the laser pulse to generate relative time delay, the pulse width of laser can be changed. The stretcher is the optical scheme to broaden the pulse width in chirp pulse amplification. By using ray trace, the pulse stretch time can be evaluated. However, due to the complicated formula of optical path in stretcher, it is difficult to obtain an analytical expression of high-order dispersion by using direct derivative. In this case, the present numerical methods are commonly used and error would be introduced into the optical system design and optimization inevitably. In this paper we introduce an analytical algorithm of stretcher dispersion. By summarizing the characteristic of stretcher formula, four fundamental functions are introduced to help to calculate the analytical derivative. By substituting the separate terms of the expressions step by step, analytical calculation of stretcher dispersion can be realized. In this paper, the ray trace of Martinez stretcher is first introduced to achieve similar phase expressions to them of existing Offner stretcher, then accurate high order dispersion results are attained by using analytical method, finally the calculation results by using the analytical method and numerical method are compared with each other. The algorithm introduced into this paper for calculating the dispersion is practical and hopeful in designing the chirp pulse amplification laser systems.