Interval Data Envelopment Analysis (Interval DEA) is a methodology to assess the efficiency of decision-making units (DMUs) in the presence of interval data. Sensitivity analysis and sustainability evaluation of decision- making units are as the most important concerns of Decision Makers (DM). In the past decades, many scholars have been attracted to the sustainability evaluation of DMUs from different perspectives. This study focuses on the sensitivity analysis in DEA and proposes an approach to determine the sustainability radius of the cost efficiency of units with interval data. Potential application of our proposed methods is illustrated by a numerical example from the literature review.