A style of coping with stress is described which has been observed in cancer patients and in highly dependent, insecurely attached individuals. This coping style includes the suppression of negative emotions and avoidance of support seeking. It is suggested that this pattern of responses is potentially dysfunctional insofar as it tends to perpetuate distress and may increase vulnerability to a broad range of illnesses. These considerations provide the basis for a provisional conceptual model, which links avoidant attachment style to the regulation of negative affect and to symptoms of psychological and physical ill‐health. This is tested on a sample of young adults under stress and predictions from the model are largely supported.