In this paper, the effect of information sharing on the dynamics of a two-stage supply chain is investigated by switched system theory and discrete system control theory. The supply chain consists of one retailer and one distributor with a kind of order-up-to policy as the control law, and where the retailer’s forecasted demands are shared with the distributor, inventory constraint is considered too. The stability area of the different modes of the supply chain is given theoretically, and bifurcation diagram are used to describe the dynamics of the system by simulations. It is pointed that information sharing can make the supply chain more stable by weaken the bullwhip effect, however, the supply chain is apt to be unstable if the retailer choose to adjust its inventory unbalance radically, if so, the distributor should take a more conservative attitude to adjust its inventory unbalance. And it is also deduced that the stock level of the distributor has the critical effect on the dynamics of the supply chain.