This thesis considers the registration of shapes, estimation of shape variability and the statistical modelling of human brain magnetic resonance images (MRI). Current shape registration techniques, such as Procrustes analysis, superimpose shapes in order to make inferences regarding the mean shape and shape variability. We apply Procrustes analysis to a subset of the landmarks and give distributional results for the Euclidean distance of a shape from a template. Procrustes analysis is then generalised to minimise a Mahalanobis norm, with respect to a symmetric, positive denite matrix, and the weighted Procrustes estimators for scaling, rotation and translation obtained. This weighted registration criterion is shown, through a simulation study, to reduce the bias and error in maximum likelihood estimates of the mean shape and covariance matrix compared to isotropic Procrustes. A Bayesian Markov chain Monte Carlo algorithm is also presented and shown to be less sensitive to prior information. We consider two MRI data sets in detail. We examine the first data set for large-scale shape dierences between two volunteer groups, healthy controls and schizophrenia patients. The images are registered to a template through modelling the voxel values and we maximise the likelihood over the transformation parameters. Using a suitable labelling and principal components analysis we show schizophrenia patients have less brain asymmetry than healthy controls. The second data set is a sequence of functional MRI scans of an individual's motor cortex taken while they repeatedly press a button. We construct a model with temporal correlations to estimate the trial-to-trial variability in the haemodynamic response using the Expectation-Maximisation algorithm. The response is shown to change with task and through time. For both data sets we compare our techniques with existing software packages and improvements to data pre-processing are suggested. We conclude by discussing potential areas for future research.