In many modern working environments interruptions are commonplace as users must temporarily suspend their current task in order to complete an unexpected intervening activity. As users are faced with more and more sources of information competing for users' attention at any time, it is becoming increasingly important to understand how interruptions affect our abilities to complete tasks. The present work introduces a new perspective for the research in the field by employing analytical, model-based, techniques that are informed by well-established cognitive theories and experimental data available in the literature. We propose stochastic modelling and model checking to predict measures of the disruptive effects of interruptions to two well-known interaction techniques: Drag 'n Drop and Speak 'n Drop. The approach also provides a way to compare the resilience of different interaction techniques to the presence of external interruptions that users need to handle. The results obtained are in a form that allows validation with results obtained by empirical studies involving real users.