A mechanism for performing probabilistic reasoning in influence diagrams using interval rather than point-valued probabilities is described. Procedures for operations corresponding to conditional expectation and Bayesian conditioning in influence diagrams are derived where lower bounds on probabilities are stored at each node. The resulting bounds for the transformed diagram are shown to be the tightest possible within the class of constraints on probability distributions that can be expressed exclusively as lower bounds on the component probabilities of the diagram. Sequences of these operations can be performed to answer probabilistic queries with indeterminacies in the input and for performing sensitivity analysis on an influence diagram. The storage requirements and computational complexity of this approach are comparable to those for point-valued probabilistic inference mechanisms.>