6Feedforward Convolutional Neural Networks (ffCNNs) have become state-of-the-art models both 7 in computer vision and neuroscience. However, human-like performance of ffCNNs does not 8 necessarily imply human-like computations. Previous studies have suggested that current ffCNNs 9 do not make use of global shape information. However, it is currently unclear whether this reflects 10 fundamental differences between ffCNN and human processing or is merely an artefact of how 11 ffCNNs are trained. Here, we use visual crowding as a well-controlled, specific probe to test global 12 shape computations. Our results provide evidence that ffCNNs cannot produce human-like global 13 shape computations for principled architectural reasons. We lay out approaches that may address 14 shortcomings of ffCNNs to provide better models of the human visual system. 15 16