Existence of redundancy in structures plays an important role in increasing their safety and reliability. However, using state-of-the-art deterministic and probabilistic approaches, all possibilities for estimation of redundancy (e.g. due to occurrence of different damage scenarios) have not been considered. One of the methods to quantify the presence of uncertainties in a system is to use interval variables. In this work, a new method for estimating the redundancy using interval structural analysis is developed. This method, hereafter referred to as Interval Redundancy Analysis (IRA), is robust and considers possibilities of strength reduction for each element leading to failure. Independent intervals for reduction of the strength for five damage scenarios of intact, slightly damage, moderately damaged, severely damaged, and completely damaged as well as strength of each element are considered. A numerical example to show the behavior of the developed method with comparison to Monte-Carlo simulation results is presented.