The mechanical behaviour of the mandibles of <i>Pan</i> and <i>Macaca</i> during mastication was compared using finite-element modelling. Muscle forces were calculated using species-specific measures of physiological cross-sectional area and scaled using electromyographic estimates of muscle recruitment in <i>Macaca</i>. Loading regimes were compared using moments acting on the mandible and strain regimes were qualitatively compared using maps of principal, shear and axial strains. The enlarged and more vertically oriented temporalis and superficial masseter muscles of <i>Pan</i> result in larger sagittal and transverse bending moments on both working- and balancing-sides, and larger anteroposterior twisting moments on the working-side. The mandible of <i>Pan</i> experiences higher principal strain magnitudes in the ramus and mandibular prominence, higher transverse shear strains in the top of the symphyseal region and working-side corpus, and a predominance of sagittal bending-related strains in the balancing-side mandible. This study lays the foundation for a broader comparative study of Hominidae mandibular mechanics in extant and fossil hominids using finite-element modelling. <i>Pan</i>'s larger and more vertical masseter and temporalis may make it a more suitable model for hominid mandibular biomechanics than <i>Macaca</i>.