This paper presents the results of a mathematical analysis of the standard assumptions used in PERT calculations. The objectives of this analysis were four-fold: (1) to pull together the mathematical aspects of the PERT model, (2) to suggest relevant analytic techniques, (3) to obtain an indication of the magnitude and direction of errors introduced by the assumptions, and (4) to suggest possible modifications and improvements in the model. The first part of the paper analyzes those assumptions relevant to the individual activities. Three possible sources of error are considered here: (1) the beta distribution assumption, (2) the standard deviation assumption and the approximation formula for the mean, and (3) the imprecise time estimates. The second part of the paper deals with the PERT network as a whole and analyzes the calculations underlying the project mean, standard deviation, and probability statements. The concept of relative criticalness is explored for the PERT stochastic model. Techniques for network reduction are outlined.