Abstract: We study a kind of stress-strength structural reliability model with stress being nested multivariate exponential distributed and strength being one-dimensional exponential distributed in this paper. On condition that strength parameter unknown and stress parameters known as well as contrary situations, the estimators \whP_A1 and \whP_A2 of the structural reliability P_A are proposed and their consistency and asymptotic normality are discussed, meanwhile, the estimators' confidence intervals are also shown. Finally, we randomly simulate the estimators \whP_A1 and \whP_A2 of P_A with the satisfactory results.