Abstract: The mathematical theory of tolerance intervals for distributions with Poisson outcomes is well developed. One criticism is the relative difficulty of computing the Poisson tolerance intervals, particularly when approximate formulae are not applicable. We offer the computational algorithm for the exact upper and lower tolerance intervals founded on the estimate of the exact confidence limits for the Poisson rate. Thus the exact tolerance intervals may be calculated using StatXact. To illustrate the algorithm, we apply it to the analysis of transfusion – associated deaths.