A basic theoretical calculation for the cylindrical and conical bent crystal spectrocgraph was done by using ray tracing method and the explicite formulations of the parameters for these spectrographs, such as spatial and spectral dispersion coordinates, linear and angular dispersion, spectral resolution, spatial and spectral magnification, lominosity, were obtained. The two kinds of spectrographs are designed and their performace is compared. The results show that the conical bent crystal spectrograph is better than the same type of the cylindrical one on the focusing properties, which improves the efficiency of light gathering, luminosity and spatial resolution. This work provids a theoretical and design basis for the future manifacturing of spectrographs.