In order to determine the extent to which the shape of the synapsid skull is adapted for resisting the mechanical loads to which it is subjected, block-or simple plate-shaped finiteelement models were constructed and loaded with external muscle and bite forces in locations estimated to resemble points of application of these forces. These 2D or 3D finite-element models were iteratively loaded and modified by removing elements that experience only low stresses, and the resulting morphologies of the models were compared with fossil skulls of synapsids and the skulls of extant mammals. The results suggest that the stress flows in these unspecific models are very similar to the arrangement of bone material in real skulls. Morphological differences between taxa depend on a few a priori conditions: length and position of the tooth rows in relation to the braincase, arrangement of muscles, position of the orbits, and position of the nasal opening. Given these initial conditions, finite-element analysis consistently reveals the close similarity between stress flows and real skulls. The major difference between mammal-like reptiles and primates is the size of the braincase. This difference accounts for most of the morphological divergence. The postorbital bar seems to be a constructional element of the skull, rather than a means to protect the eyes. The skull shapes of higher primates are determined mainly by masticatory forces and less by external forces acting on the head. This study demonstrates the utility of finite-element modeling for testing hypotheses regarding relationships between form and function in vertebrate skulls. Key words: functional morphology; opossum; snapping; Lemuriformes; gorgonopsians; therocephalians; finite-element analysis; synthesis of skull shapeThe research reported here is part of a long-term research program seeking to determine whether and to what extent the shape of the vertebrate skull is adapted for resisting the mechanical loads to which it is subjected by biting, the weight of the head and loads carried between the jaws, and accelerations associated with movements. The ultimate question is: What are the reasons for the development of skull shape in evolution and ontogeny? This research program does not seek to find out how the existing skull of a crocodile, a galago, or a macaque behaves under load (see, e.g., Metzger et al., 2005, this issue; Strait et al., 2005, this issue;, this issue), but rather why the various skull shapes have evolved. In terms of evolutionary theory, the question is:Which selective pressures may have led to the development of specific skull morphologies? This approach is based on empirical information, but the way in which the