In a water distribution system, low or negative pressure may occur under normal operation of the system and may lead to contaminant intrusion. To assess the risk associated with contaminant intrusion, exposure assessment is required. To have more accurate intrusion exposure assessment, the effects of the surrounding soil on the intrusion rate must be considered. This research proposes a model to create a more realistic estimation of intrusion rate. A two‐level factorial design was used to screen the effect of pipe internal pressure, soil porosity, average diameter of soil particles, size of the leak point, and pipe burial depth. The Buckingham p theorem was applied to group the influential factors into a set of dimensionless p parameters. The relationship among the p parameters was obtained by using the numerical data generated by a two‐dimensional finite element model for flow in a saturated zone surrounding a pipe. A regression analysis was then applied to find the best fit for the data.