The concrete delivery and pumping process is a stochastic system. if analysed deterministically there is the danger that the negative effects of the random distribution of events are not taken into account, leading to poor estimates of production and cost. By representing the system as a random process the construction engineer can, first, achieve improved estimates of the overall productivity and thus schedule deliveries better, and, secondly, determine the effect of unanticipated events such as excessive delivery or pour times. This paper presents a stochastic model of the delivery and pumping of concrete. By investigating data gathered from a major civil engineering project, the random nature of the process has been represented within the model by means of the gamma probability distribution. The model has been analysed using discrete-event simulation techniques, which have been used successfully in other civil and production engineering applications. Experimental analysis of the model has indicated that it can provide estimates of the performance of concreting operations that are more realistic than those obtained if the system is analysed on a non-random basis. The main conclusion is that for every concreting operation there is an optimal combination of truck interarrival and concrete pump times that will maximize the utilization of the plant and minimize the duration of the operation. This optimal cannot be calculated deterministically and is different from that derived from the non-random model.