An ARX(Auto-Regressive eXogenous) modeling technique for vortex dynamics in the BFS(Backward Facing Step) flow field is proposed in this paper. In order for the modeling of the dynamics, the spatial and temporal modes are extracted through POD(Proper Orthogonal Decomposition) analysis. Determining the orders of the inputs and outputs for an ARX structure is carried out by the spectrum analysis and temporal mode analysis, respectively. The order of input delay terms is also determined by the flow velocity. Finally the coefficients of the ARX model are designed by using an artificial neural network.