We review the characteristics of signalling storms that have been caused by certain common apps and recently observed in cellular networks, leading to system outages. We then develop a mathematical model of a mobile user's signalling behaviour which focuses on the potential of causing such storms, and represent it by a large Markov chain. The analysis of this model allows us to determine the key parameters of mobile user device behaviour that can lead to signalling storms. We then identify the parameter values that will lead to worst case load for the network itself in the presence of such storms. This leads to explicit results regarding the manner in which individual mobile behaviour can cause overload conditions on the network and its signalling servers, and provides insight into how this may be avoided.