Brain convolutions are a specificity of mammals. Varying in intensity according to the animal species, it is measured by an index called the gyrification index, ratio between the effective surface of the cortex compared to its apparent surface. Its value is close to 1 for rodents (smooth brain), 2.6 for newborns and 5 for dolphins. For humans, any significant deviation is a signature of a pathology occurring in fetal life, which can be detected now by magnetic resonance imaging (MRI). We propose a simple model of growth for a bilayer made of the grey and white matter, the grey matter being in cortical position. We analytically solved the neo-Hookean approximation in the short and large wavelength limits. When the upper layer is softer than the bottom layer, the selection mechanism is shown to be dominated by the physical properties of the upper layer. When the anisotropy favors the growth tangentially as for the human brain, it decreases the threshold value for gyri formation. The gyrification index is predicted by a post-buckling analysis and compared with experimental data. We also discuss some pathologies in the model framework.