DescriptionWhat makes two shapes similar? Given two shapes, is there a mathematically principled way to predict human similarity judgments, and consequent shape classification judgments? To answer this question, an experimental framework was developed for rapidly collecting human judgments of whether shapes did or did not belong to novel shape categories. The subjects’ judgments of category membership were compared against the predictions of several different shape similarity/classification models. Among these models, I propose a new lattice similarity model of shape similarity based on Bayesian shape skeletons. An earlier model of similarity based on the same Bayesian shape skeletons, the cross likelihood, has been shown to be an effective predictor of human shape discrimination, but this model applies only to shapes with similar part structures. The lattice similarity model is more principled and general, and is suitable for comparing arbitrary shape pairs in both 2D and 3D domains. This new model provides a better overall fit to human data than a number of competing models, including the cross likelihood model, an out-of-the-box convolutional neural network model, and a non-skeletal part-based similarity model proposed by Erdogan and Jacobs (2017). The lattice similarity model predicted human data more accurately than all other tested models in experiments that used 3D shapes, and most other models in experiments that used 2D shapes. Prototype-like and exemplar-like versions of the lattice similarity model were also compared using the same human data as above; the prototype-like version fits the experimental data better than the exemplar-like version.