The choice among alternative water supply sources is generally based on the fundamental objective of maximising the ratio of benefits to costs. There is, however, a need to consider sustainability, the environment and social implications in regional water resources planning, in addition to economics. In order to achieve this, multi-criteria decision analysis (MCDA) techniques can be used. Various sources of uncertainty exist in the application of MCDA methods, including the selection of the MCDA method, elicitation of criteria weights and assignment of criteria performance values. The focus of this paper is on the uncertainty in the criteria weights. Sensitivity analysis can be used to analyse the effects of uncertainties associated with the criteria weights. Two existing sensitivity methods are described in this paper and a new distance-based approach is proposed which overcomes limitations of these methods. The benefits of the proposed approach are the concurrent alteration of the criteria weights, the applicability of the method to a range of MCDA techniques and the identification of the most critical criteria weights. The existing and proposed methods are applied to three case studies and the results indicate that simultaneous consideration of the uncertainty in the criteria weights should be an integral part of the decision making process.