Abstract: In this paper, the exact Bayes limits for safety factor of structural reliability for the conjugate prior distribution are derived when one of two coefficients Cx (coefficient of variation of strength) and Cy (coefficient of variation of load) is unknown Which are given by the nonlinear equation for CDF of generalized noncentral t-distribution, When the noninformative prior distribution is taken on normal distribution, the exact Bayes limits are equal to the exact Fiducial limits The tables of upper limits of the safety factor for structural reliability design are computed .Meanwhile the integral equation for upper limits of the safety factor when both Cx and Cy are unknown is present and the method is illustrated.