Unrest at large calderas rarely ends in eruption, encouraging vulnerable communities to perceive emergency warnings of volcanic activity as false alarms. A classic example is the Campi Flegrei caldera in southern Italy, where three episodes of major uplift since 1950 have raised its central district by about 3 m without an eruption. Individual episodes have conventionally been treated as independent events, so that only data from an ongoing episode are considered pertinent to evaluating eruptive potential. An implicit assumption is that the crust relaxes accumulated stress after each episode. Here we apply a new model of elastic-brittle failure to test the alternative view that successive episodes promote a long-term accumulation of stress in the crust. The results provide the first quantitative evidence that Campi Flegrei is evolving towards conditions more favourable to eruption and identify field tests for predictions on how the caldera will behave during future unrest.