Understanding the biomechanical mechanisms by which the cerebral cortex folds is a fundamental problem in neuroscience. Current mathematical models of cortical folding do not include three dimensional geometry or measurement of cortical growth in developing brains extracted from experimental data. We present two biomechanical models of cortical folding which integrate 3D geometry and information taken from MRI scans of fetal sheep brains at a number of key developmental stages. The first model utilises diffusion tensor imaging (DTI) measurements of white matter fibre orientation in the fetal sheep brains as a cue to the tension forces that may regulate folding. In the second model, tangential cortical growth is modelled by osmotic expansion of the tissue and regulated by inhomogeneous white matter rigidity as a biomechanism of cortical folding. This is based on quantitative analysis of cortical growth and inhomogeneous white matter anisotropy measured from the MRI data. We demonstrate that structural and diffusion tensor MRI can be combined with finite element modelling and an explicit growth mechanism of the cortex to create biologically meaningful models of the cortical folding process common to higher order mammals.