Understanding brain mechanics is crucial in the study of pathologies involving brain deformations such as tumor, strokes, or in traumatic brain injury. Apart from the intrinsic mechanical properties of the tissue, the topology and geometry of the mammalian brains are particularly important for the mechanical response of the brain. We use computational methods in combination with geometric models to understand the role of these features. We find that the geometric quantifiers such as the gyrification index play a fundamental role in the overall mechanical response of the brain.We further demonstrate that topological diversity in brain models is more important than differences in mechanical properties: Topological differences modify not only the stresses and strains in the brain but also its spatial distribution. Therefore, computational brain models should always include detailed geometric information to generate accurate mechanical predictions. These results suggest that mammalian brain gyrification acts as a damping system to reduce mechanical damage in largemass brain mammals.Our results are relevant in several areas of science and engineering related to brain mechanics, including the study of tumor growth, the understanding of brain folding, and the analysis of traumatic brain injuries.