For the sake of describing route choice behavior of travelers under degradable network with elastic demand and providing decision references for travelers and managers, the dynamic generalized travel cost is defined as the weighted sum of travel time, travel time reliability and monetary cost. Due to random variations of road networks, travelers are assumed to choose their optimal routes while their generalized travel costs are minimized. Under those assumptions, a stochastic user equilibrium model based on dynamic generalized travel cost is developed. The MSA (method of successive average) algorithm for the model is also proposed. Through a test on an example road network, numerical results show that travelers’ risk attitudes, degradation factor and monetary cost have significant influences on road traffic assignment. It is consistent with practical experiences, so it illustrates that the presented stochastic user equilibrium model based on dynamic generalized travel cost can truly reflect travelers route choice behavior on stochastic road network.