Inter-domain routing is the most critical function of the Internet. The routing system is a logical network relying on the physical infrastructure with geographical characteristics. Nature disasters or disruptive accidents such as earthquakes, cable cuts and power outages could cause regional failures which fail down geographically co-located network nodes and links, therefore, affect the resilience of inter-domain routing system. This paper presents a model for regional failures in inter-domain routing system called REFER for the first time. Based on REFER, the resilience of the inter-domain routing system could be evaluated on a finer level of the Internet, considering different routing policies of intra-domain and inter-domain routing systems. Under this model, we perform simulations on an empirical topology of the Internet with geographical characteristics to simulate a regional failure locating at a city with important IXP (Internet eXchange Point). Results indicate that the Internet is robust under a city-level regional failure. The reachability is almost the same after the failure, and the reroutings occur at the edge of the Internet, hardly affecting the core of inter-domain routing system.