Time geography is a powerful framework for analyzing human activities under various space–time constraints. At the core of time geography is the concept of the space–time prism, which delimits an individual's potential activity locations in space and time. The classical space–time prism, however, admits only deterministic travel speeds and ignores the stochastic nature of travel environments. In this article, the classical space–time prism model is extended to congested road networks with travel time uncertainty. A reliable space–time prism is proposed to consider explicitly an individual's on-time arrival probability concerns in the face of travel time uncertainty. The reliable space–time prism is defined as the set of space–time locations where an individual can participate in an activity and return to his or her destination with a given on-time arrival probability. To construct such a reliable space–time prism in a road network, a solution algorithm is developed. A case study using real-world traffic information is carried out to demonstrate the applicability of the proposed prism model. The results of the case study indicate that the proposed prism model can represent well individuals’ space–time taking into account various on-time arrival probability concerns.