Abstract: In aseismic design of reinforced concrete structures, “strong shear weak bending” is an important design conception to guarantee the ductibility of the structure. The interval variable is introduced to express the epistemic uncertainty and the failure probability interval of reinforced concrete column is analyzed. The mathematic description of uncertainty is fulfilled by integration of the interval variable and random variable that represents the epistemic and aleatory uncertainty, respectively. The interval-valued probabilistic reliability model for “strong shear weak bending” is formulated according to the inclusion relation of the element events and the failure event. The equivalence relation between the belief-plausibility function and the upper-lower boundaries of failure probability interval is verified by the evidence theory as well. For the computation of the resistance capability involving interval-valued uncertain parameters, Berz-Taylor model is introduced to reduce the error induced by interval inflation. The simulated annealing genetic algorithm (SAGA) is applied to determine the approximate design interval of the “strong shear weak bending” in numerical simulation. A specific sampling function constructed by such design interval is adopted to gain the failure probability interval; error analysis indicates that the precision of the method is acceptable. Finally, simulated data analysis is carried out on the different design parameters affecting the reliability and corresponding design suggestions are proposed.