The finite element analysis（ FEA） model of silicon nitride ceramic ball bearing is established by ANSYS Workbench based on Hertz theory assumption,the contact stress distribution between rolling bodies and rings are attained,the FEA calculation results and Hertz contact theory can match well,which illustrates the correctness of the finite element analysis model. On this basis,the Rotating load and friction are applied to the FEA model to overcome the limitation of the Hertz contact theory,the contact stress distribution of the bearing under complicated working conditions is obtained. Taking the maximum contact stress as the objective function,the curvature radius of the inner and outer rings are optimized by using the direct optimization method.After optimization,the maximum contact stress of the bearing is decreased by 9. 21%.