This article explores the relations between network properties and the effect from moving rainstorms in terms of the peak response and time to centroid of hydrographs. A simple conceptual rectangular catchment is introduced with different configurations of drainage network simulated by the Gibbs stochastic model. The efficiency of the urban pipe networks varies widely compared with natural river networks; hence, the Gibbs model can be an appropriate approach to represent the network properties in urban drainage system. Simple cases of rainstorms moving with upstream and downstream directions and different speeds are considered to investigate the effect of rainstorm movement on urban drainage network runoff hydrographs. The results indicate that the effect of the direction and speed of the rainstorm movement varies significantly depending on the network properties. The relationship between storm speed and direction and the change in the peak runoff is dependent on the network configuration and network efficiency. In contrast to previous studies, this study indicates that the speed and direction of the rainfall movement that produces the maximum peak discharge changes depending on the network configuration. Copyright © 2011 John Wiley & Sons, Ltd.