Making decisions under conditions of uncertainty is a challenging task, yet is not uncommon when engineering or management alternatives are evaluated through criteria of social and environmental sustainability. ELECTRE III is a widely-used multi-criteria decision method for ranking alternatives. The method accounts for uncertainty in criteria values by including pseudo-criteria; usually, an indifference, preference and veto thresholds are set for each criteria. Decision makers are also required to provide criteria weights signify each criterion's importance. However, choosing realistic values for each threshold remains a difficult task. Moreover, criteria weightings are known to be a major factor affecting the end result of the ranking exercise. This paper, presents a modified version of ELECTRE III, called ELECTRE-SS, that utilises stochastic techniques to account for uncertainty in the weightings and threshold values of criteria. The method can be particularly useful when a large number of stakeholders are involved in the decision-making process. The method is described and validated and its scope illustrated thorough case problems.