Abstract: Uncertain parameters are described as interval numbers, then, the reliability index equations of bar structures are obtained. A modified matrix affine arithmetic polynomial evaluation method, together with recursive derivative information, is proposed in this paper. Recognizing that affine forms and intervals variables can transform each other, affine forms of bounded uncertain variables and modified affine arithmetic including derivative information for univariate interval polynomial evaluation are introduced into the modeling and calculating of non-probabilistic reliability index. A hanger beam and a ten-bar truss structure are analyzed to illustrate the validity and feasibility of the presented procedures.