A technique is presented to assist in the scheduling of projects given uncertainties (i.e. tolerances) on the durations of activities in the project. A Monte Carlo analysis is carried out in the tolerance region of activity durations and performance functions of interest such as the mean and variance of project duration and probability-weighted critical paths are evaluated. The proposed technique has a number of advantages. First, it handles the situation where activities are not independent. Second, in deducing variations in project duration, account is taken of all toleranced activities in the project. This is in contrast to existing methods which take account only of activities on the critical path. Third, the technique not only identifies critical paths, but also estimates the probability that those paths remain critical given the tolerance variations in the project. By virtue of the statistical sampling approach, computational cost of the technique is independent of project complexity. Application of the technique is a vital pre-requisite for optimal project scheduling, moreover, preliminary studies have shown that valuable sensitivity information regarding project duration and critical paths can be obtained.