It has long been recognised that phrases and sentences are organised hierarchically, but many computational models of language treat them as sequences of words without computing constituent structure. Against this background, we conducted two experiments which showed that participants interpret ambiguous noun phrases, such as second blue ball, in terms of their abstract hierarchical structure rather than their linear surface order. When a neural network model was tested on this task, it could simulate such “hierarchical” behaviour. However, when we changed the training data such that they were not entirely unambiguous anymore, the model stopped generalising in a human-like way. It did not systematically generalise to novel items, and when it was trained on ambiguous trials, it strongly favoured the linear interpretation. We argue that these models should be endowed with a bias to make generalisations over hierarchical structure in order to be cognitively adequate models of human language.