Serious and debilitating symptoms of anxiety are the most common mental health problem worldwide, accounting for around 5% of all adult "years lived with disability in the developed world". Avoidance behaviour - avoiding social situations for fear of embarrassment, for instance - is a core feature of such anxiety. However, as for many other psychiatric symptoms, the biological mechanisms underlying avoidance remain unclear. Reinforcement-learning models provide formal and testable characterizations of the mechanisms of decision-making; here, we examine avoidance in these terms. One hundred and one healthy and pathologically anxious individuals completed an approach-avoidance go/no-go task under stress induced by threat of unpredictable shock. We show an increased reliance in the anxious group on a parameter of our reinforcement-learning model that characterizes a prepotent (Pavlovian) bias to withhold responding in the face of negative outcomes. This was particularly the case when the anxious individuals were under stress. This formal description of avoidance within the reinforcement-learning framework provides a new means of linking clinical symptoms with biophysically plausible models of neural circuitry and, as such, takes us closer to a mechanistic understanding of pathological anxiety.