Mobile networks are vulnerable to signaling attacks and storms that are caused by traffic patterns that overload the control plane, and differ from distributed denial of service attacks in the Internet since they directly affect the control plane, and also reserve wireless bandwidth and network resources without actually using them. Such storms can result from malware and mobile botnets, as well as from poorly designed applications, and can cause service outages in 3G and 4G networks, which have been experienced by mobile operators. Since the radio resource control (RRC) protocol in the 3G and 4G networks is particularly susceptible to such storms, we analyze their effect with a mathematical model that helps to predict the congestion that is caused by a storm. A detailed simulation model of a mobile network is used to better understand the temporal dynamics of user behavior and signaling in the network and to show how RRC-based signaling attacks and storms cause significant problems in both the control and user planes of the network. Our analysis also serves to identify how storms can be detected, and to propose how system parameters can be chosen to mitigate their effect.