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In the current paper, the effect of tensile softening parameters, the tensile strength σt and the initial slope k1 of the stress-crack width curve, on the structural size-effect law in bending of concrete are studied by a bending model. The model results show that the size-effect law in bending strength normally presented by flexural strength and beam height diagram (σf-logH) is strongly dependent on σt and k1. With increase of beam height, the general size-effect law in bending can be characterised as a fast reduction stage followed by a stable decreasing stage and finally converged to the tensile strength of concrete. With increasing tensile strength, the σf-logH curve goes up and the value of dσf/dlogH gradually increases. In the meantime, for a given beam height, bending strength increases with increase of k1. The model predictions are compared with experimental results. Good agreement between model predictions and experiments has been obtained. [ABSTRACT FROM AUTHOR]