In many modern working environments interruptions are commonplace as users must temporarily suspend a task to complete an unexpected intervening activity. As users are faced with more and more sources of information competing for their attention, it is becoming increasingly important to understand how interruptions affect their abilities to complete tasks. This paper introduces a new perspective for research in this 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 obtained results are in a form that allows validation with results obtained by empirical studies involving real users.