Brain development is a dynamic process with tissue-specific alterations that reflect complex and ongoing biological processes taking place during childhood and adolescence. Accurate identification and modelling of these anatomical processes in vivo with MRI may provide clinically useful imaging markers of individual variability in development. In this study, we use manifold learning to build a model of age- and sex-related anatomical variation using multiple magnetic resonance imaging metrics. Using publicly available data from a large paediatric cohort (n = 768), we apply a multi-metric machine learning approach combining measures of tissue volume, cortical area and cortical thickness into a low-dimensional data representation. We find that neuroanatomical variation due to age and sex can be captured by two orthogonal patterns of brain development and we use this model to simultaneously predict age with a mean error of 1.5-1.6 years and sex with an accuracy of 81%. We validate this model in an independent developmental cohort. We present a framework for modelling anatomical development during childhood using manifold embedding. This model accurately predicts age and sex based on image-derived markers of cerebral morphology and generalises well to independent populations.