A study and design of one-dimensional model for optical cavity of free electron laser has been presented in this work by using a computer program and Matlab 6.5 or 6.1 languages. This work deals with the linear mode of operation. The effects of the radius of curvature of mirrors, cavity length, radiation wavelength, undularor wavelength, Rayliegh length and slippage distance on the optical cavity have been studied. It is found that the beam waist is 1.9mm and Rayliegh length is 1.2m, which depends on the resonator “g” parameter, the cavity length and the radius of curvature of mirror of the optical resonator. The beam waist decreases with the decrease of both radius of curvature of mirror and cavity length. The slippage distance and the gain decrease when the number of undulator periods inside the cavity decreases. The maximum gain is 2.21*104 when the optimum output coupling reached 17.3% Finally, according to this study, an optical resonator has been designed for new undulator.