One of the most highly touted virtues of knowledge-based expert systems is their ability to construct explanations for their lines of reasoning. However, there is a basic difficulty in generating explanations in expert systems that reason under uncertainty using numeric measures. In particular, systems based upon evidential reasoning using the theory of belief functions have lacked all but the most rudimentary facilities for explaining their conclusions. In this paper we review the process whereby other expert system technologies produce explanations, and present a methodology for augmenting an evidential-reasoning system with a versatile explanation facility. The method, which is based on sensitivity analysis, has been implemented, and several examples of its use are described.