This study developed a variable demand traffic assignment model by stable dynamics. Stable dynamics, suggested by Nesterov and do Palma[19], is a new model which describes and provides a stable state of congestion in urban transportation networks. In comparison with the user equilibrium model, which is based on the arc travel time function in analyzing transportation networks, stable dynamics requires few parameters and is coincident with intuitions and observations on congestion. It is therefore expected to be a useful analysis tool for transportation planners. In this study, we generalize the stable dynamics into the model with variable demands. We suggest a three stage optimization model. In the first stage, we introduce critical travel times and dummy links and determine variable demands and link flows by applying an optimization problem to an extended network with the dummy links. Then we determine link travel times and path flows in the following stages. We present a numerical example of the application of the model to a given network.