This paper addresses the question of how close mammalian teeth are to ideal functional forms. An ‘ideal’ form is a morphology predicted to be the best functional shape according to information of the relationships between shape and function. Deviations from an ideal form are likely to indicate the presence of developmental or genetic constraints on form. Model tools were constructed to conform to functional principles from engineering and dental studies. The final model shapes are very similar to several mammalian tooth forms (carnassial teeth and tribosphenic-like cusps), suggesting that these tooth forms very closely approach ideal functional forms. Further evidence that these tooth forms are close to ideal comes from the conservation over 140 million years, the independent derivation and/or the occurrence over a size range of several orders of magnitude of these basic tooth forms. One of the main functional shapes derived here is the ‘protoconoid’, a fundamental design for double-bladed tools that fits a large number of functional parameters. This shape occurs in tooth forms such as tribosphenic, dilambdodont and zalambdodont. This study extends our understanding of constraints on tooth shape in terms of geometry (how space influences tooth shape) and function (how teeth divide food). © 2003 The Linnean Society of London. Biological Journal of the Linnean Society, 2003, 78, 173–191.