Abstract Statistical analyses of geometric morphometric data have been generally restricted to the Euclidean space tangent to curved shape space. This approach is based on the knowledge that such an approximation does not affect statistical and biological conclusions, when differences among specimens' shapes are not too large. We examined the wide variation of shapes within the vertebrate class Mammalia to determine the tangent space approximation by comparing Procrustes distances in Kendall shape space to tangent space distances among 53 mammal skulls and articulated jaws belonging to almost all of the living orders. Previous studies have been restricted to relatively low taxonomic levels, implying a narrower range of shapes. Thirty-five three-dimensional (3D) landmarks on the sagittal plane and right side of each specimen were digitized using a MicroScribe 3DX. Procrustes and tangent space distances between all specimens were compared using the program TPSSMALL (Rohlf, 1998b). The correlations between these distances were always greater than 0.99. Lower jaw and brain subsets of the landmarks gave similar results, while the face subset had more scatter, but nearly the same correlation. The 3D shapes, as summarized by the landmarks, were clustered and the dendrogram was compared to a currently hypothesized phylogeny. We also point out that data from landmark morphometrics are as appropriate as morphological and molecular data for cladistic analysis.