The secondary palate of mammals is a bony shelf that closes the ventral aspect of the rostrum. The rostrum, therefore, approximates to a tapered semicylindrical tube that is theoretically a mechanically efficient structure for resisting the forces of biting, including the more prolonged bouts of mastication typical of mammals. Certain mammal-like reptiles illustrate stages in the development of the palate in which the shelves projecting medially from each premaxilla and maxilla do not meet in the midline. We evaluate several geometric properties of sections through the rostrum of the American opossum (Didelphis virginiana). For loading at the incisors and canines, these properties indicate the structural strength and stiffness in both bending and torsion of the rostrum and of single maxillae. We then repeat the analysis but progressively omit segments of the palatal shelf, a procedure which simulates, in reverse, the evolutionary development of the structure. The results demonstrate that the secondary palate contributes significantly to the torsional strength and stiffness of the rostrum of Didelphis and to the strength of each maxilla in lateromedial bending. The major evolutionary implications of the results are that the rapid increase in rostral strength with small increments of the palatal shelves may have been a significant factor in the development of the complete structure. The results indicate that there was a marked jump in torsional strength and stiffness when the shelves met in the midline, which is likely to have been important in the subsequent development of the diverse masticatory mechanisms of cynodonts and mammals. On the basis of this analysis the mammalian secondary palate may be interpreted as one of a number of methods, seen in the mammal-like reptiles, for strengthening the rostrum.