Glires (rodents, lagomorphs and their fossil kin) is the most speciose and arguably most diversified clade of living placentals. Different lineages within the Glires evolved basically opposite chewing movements: a mostly transversal power stroke in lagomorphs, and a mostly proal power stroke in rodents, but the ancestral condition for Glires is still unclear. To address this knowledge gap, we studied the mandibles of Chinese Palaeocene Glires representing the duplicidentate (lagomorph-like;Mimotona) and simplicidentate (rodent-like;EomylusandHeomys) lineages. To assess the mechanical resistance of mandibles to bending and torsion, we calculated the section modulus. The dentaries differ greatly in morphology and the region where the maximum grinding force was likely applied. The early PalaeoceneMimotona liiand the middle PalaeoceneMimotona robustaandHeomys orientalisall show a pattern of increasing strength moving posteriorly along the mandible, similar to sciurids and the mountain beaver. By contrast, the late PalaeoceneEomylussp. mandible was strongest in the m1 region, a pattern seen in lagomorphs and the stem placentalZofialestes. Our results indicate the early diversification of mandible structure of Glires, demonstrate a mixture of duplicidentate and simplicidentate characters among the basal Glires and suggest an early occurrence of a lagomorph-like morphotype.This article is part of the theme issue ‘The mammalian skull: development, structure and function’.