Abstract: The non-probabilistic reliability problem of structures with uncertain parameters bounded by ellipsoidal convex models is investigated, and a non-probabilistic reliability model is proposed. Further the ratio of the volume of safe region to the total volume of the basic variable region is utilized as the measurement of the structural reliability, and the compatibility of the proposed non-probabilistic reliability model with the probabilistic reliability model is proved. In the case of interval vector determined by the ellipsoid from the uncertain parameter vector, the functional relation between the non-probabilistic reliability model based on the ellipsoidal convex model and the non-probabilistic reliability model based on the interval model is shown. The results from two numerical examples indicate that the non-probabilistic reliability based on interval model is more conservative than that based on ellipsoidal convex model.