Brain shape might influence cognitive performance because of the relationships between functions, spatial organization, and differential volumetric development of cortical areas. Here we analyze the relationships between midsagittal brain shape variation and a set of basic psychological measures. Coordinates in 2D from 102 MRI-scanned young adult human brains were superimposed through a Procrustes approach, and the residual variation was regressed onto 21 cognitive tests performed by the same individuals. Most of the composite and specific variables (including general intelligence, working memory, attention, and executive functions) do not show meaningful correlations with midsagittal brain morphology. However, variables related to mental speed display subtle but consistent correlations with brain shape variation. Such correlations are small, suggesting that the influence of midsagittal brain geometry on individual cognitive performance is negligible. Nevertheless, this evidence can supply information on brain biology and evolution. Areas associated with the parietal cortex appear to be involved in relationships between brain geometry and mental speed. These areas have been associated with relevant endocranial differences between living and extinct humans, and are important as functional and structural components of brain organization. The limited correlation between brain geometry and mental speed among modern individuals might be more relevant when the large paleoneurological variation of the genus "Homo" is taken into account.