Endocranial casts are commonly used to infer the shape, size, asymmetry or overall organization of the brain of fossil species. However, endocasts are only an indirect representation of the brain. Few studies seek to assess the faithfulness of this representation, upon which is based much of our knowledge on the evolution of the brain of hominids. The aim of this work is to automatically map in 3D the distance between the brain and the inner surface of the skull in humans and other primates to see how some morphological characteristics of the endocast (and in particular its asymmetries) relate to those of the brain. MR images are used to automatically extract the brain and virtual endocast. Point-to-point distances are evaluated between the two surfaces to generate a distance map. Bilateral asymmetries of the brain and virtual endocast are also computed. A mean endocranial shape evaluation provides average distances and asymmetries maps. Results show that the local distance between the brain and the virtual endocast strongly varies between anatomical regions, but symmetrically with respect to the mid-sagittal plane. It follows that global asymmetries of the brain and endocast are closely related. These findings suggest that in paleoanthropology, the study of natural or virtual endocasts gives significant information about the morphology of the brain of fossil species. Moreover, we may use the distance map computed on extant species to infer more precise information about the potential surface of the brain of fossil species.