To address sustainability issues, concrete design and specification must consider a variety of evaluation criteria, necessitating analytical methods that can optimize mixes to meet performance requirements while maximizing sustainability. This paper proposes the desirability approach, a multi-response optimization technique, as a new method for the sustainability evaluation of concrete materials. A demonstration study, using four sustainability indicators and six concrete mixes with varying binder compositions and aggregate types, is presented that explores how changing the shape of the desirability function, which translates indicator values to desirability, affects the sustainability evaluation output. Treating the function shapes as a source of uncertainty, sustainability evaluation is conducted with uncertainty analysis to produce a sustainability score distribution for each mix, which is described by statistical measures. Mixes with the highest and lowest indicator values exhibited the least variance in their scores, as these values were unaffected by the function shape. Sensitivity analysis, which measures the contribution of the sources of uncertainty to the total output uncertainty, found that the interactions when varying multiple function shapes simultaneously were the most influential source of uncertainty, which may be caused by multi-collinearity among the indicators. It was also found that sustainability scores calculated by geometric aggregation were lower than those calculated by linear aggregation.