In recent years, cellular networks have been reported to be susceptible targets for Distributed Denial of Service (DDoS) attacks due to their limited resources. One potential powerful DDoS attack in cellular networks is a SMS flooding attack. Previous research has demonstrated that SMS-capable cellular networks are vulnerable to a SMS flooding attack in which a sufficient rate of SMS messages is sent to saturate the control channels in target areas. We propose a novel detection algorithm which identifies a SMS flooding attack based on the reply rate to messages sent by a handset. We further propose a mitigation technique to reduce the blocking rate caused by the attack. Our simulation results show that the false positive and false negative rates of our detection algorithm are low even when the attack traffic is blended with flash crowd traffic and/or the attack traffic mimics flash crowd traffic, and that the blocking rate is successfully reduced through the mitigation technique.