Chirped Mo/Si multilayer mirrors used in 13-17nm region have been designed using analytical approach based on the combination of genetic algorithm and simplex algorithm. The Cauchy equation and the polynomial expression were used to fit the real part and the imaginary part of the optical constants of Mo and Si in the wavelength region of 12.8-17.2nm, respectively. The reflectivity, reflective phase, group delay and group delay dispersion of the multilayer were calculated based on the Fresnel iterative equations. The initial structure of the multilayer was obtained by using the genetic algorithm, and the final structure of the mirror was optimized by using the simplex algorithm. We got the different multilayer mirrors for the target GDD of -2800 as2, -3600 as2, and -6500 as2. For these three multilayer mirrors, the average reflectivities in the wavelength range of 13-17 nm are 7.00± 0.08 %, 5.99 ±0.05 %, and 6.00±0.05 %, respectively. And the average GDD in the same wavelength range are -2793.22±104.00 as2,-3597.44±79.06 as2, and - 6498.13±59.96 as2. In addition, the effects of the interface roughness on the reflectivity and the phase were discussed. It is found that the reflectivity is sensitive to the interface roughness, but the phase is insensitive.© (2010) COPYRIGHT SPIE--The International Society for Optical Engineering. Downloading of the abstract is permitted for personal use only.