Segmentation of large 3D medical datasets, as resulting for example from routine Magnetic Resonance Imaging (MRI) investigations is one of the basic problems of the medical image analysis. This paper presents a novel approach that combines the desirable properties of physical models (snakes), shape representation by Fourier parametrization (Fourier snakes), and modelling of natural shape variability for a new model-based segmentation technique. Flexible shape models are represented by a parameter vector describing the mean contour and by a set of eigenmodes of the parameters characterizing the shape variation. The segmentation process is divided into an initial placing of the mean model and an elastic deformation restricted to the model variability. A first implementation separates shape changes due to global similarity transforms from small-scale biological variation by providing elastic deformations of normalized model contours only. The performance was considerably improved by building shape models normalized with respect to a small set of stable landmarks and by explaining the remaining variability among a series of images with the model flexibility. The initial placement is solved by a new coarse-to-fine procedure based on the set of deformation eigenmodes. The extension to 3-D is severely impeded by finding a proper surface parametrization for arbitrary objects with spherical topology. We apply a newly developed surface parametrization which achieves a uniform mapping between object surface and parameter space. The 3D model building and Fourier-snake procedure is used fo segmenting deep structures of the human brain from MR volume data.