Using three-dimensional, digitized data of the crania and maxillary teeth of seventeen theropod dinosaurs, biomechanical analysis reveals a series of interrelated correlations between the sizes, orientations, and ellipticity (narrowness) of the orbits and the inferred mechanical properties of the skull and teeth that relate to biting. A value for the sagittal bending strength of a cranium was computed at the longitudinal position of the orbit under an assumed load applied at the longitudinal position of the longest maxillary tooth. With the area of the orbit expressed as a percentage of the total lateral area of the skull, an inverse relationship was found to exist between the area of the orbit and the bending strength of the skull. Orbits with long-axis inclination angles in the range of 150° ± 15° are associated with taxa possessing small teeth and relatively weak skulls. Orbits with inclinations in the range of 95° ± 10° are associated with taxa possessing relatively strong skulls and long and/or strong teeth. In weak-skulled taxa, the long axes of the orbits are orientated at angles of not less than 45° to the mean inclination direction of the maxillary teeth. In strong-skulled taxa, the long axes of the orbits are sub-parallel to mean maxillary tooth direction. Finally, the ellipticity of the orbits are positively correlated with the strengths of skulls. It is proposed that the form of the orbital opening in theropods with strong skulls is governed by the requirements of the posterior half of the skull to resist the muscle generated forces associated with prey capture and/or dismemberment.