Previous work has suggested the existence of differences between the cerebral cortex of normal individuals, and those of patients with diseases such as epilepsy and schizophrenia. These shape abnormalities may be of developmental origin. Improved shape measures could provide useful tools for neuroscience research and patient diagnosis. We consider the theoretically desirable properties of measures of brain shape. We have implemented seven measures, three from the neuroscience literature, and four new to this field. Three of the measures are zero-order and four are second-order with respect to the surface. We validate the measures using simple geometrical shapes, and a collection of magnetic resonance scans of ten histologically normal ex vivo fetal brains with gestational ages from 19-42 weeks. We then apply the measures to MR scans from two histologically abnormal ex vivo brains. We demonstrate that our implementation of the measures is sensitive to anatomical variability rather than to the discreteness of the image data. All the measures were sensitive to changes in shape during fetal development. Several of the measures could distinguish between the normal and abnormal fetal brains. We propose a multivariate approach to studying the shape of the cerebral cortex, in which both zero-order and second-order measures are used to quantify folding.