A considerable biomechanical challenge faces larger terrestrial animals as the demands of body support scale with body mass (Mb), while muscle force capacity is proportional to muscle cross-sectional area, which scales with Mb2/3. How muscles adjust to this challenge might be best understood by examining varanids, which vary by five orders of magnitude in size without substantial changes in posture or body proportions. Muscle mass, fascicle length and physiological cross-sectional area all scale with positive allometry, but it remains unclear, however, how muscles become larger in this clade. Do larger varanids have more muscle fibres, or does individual fibre cross-sectional area (fCSA) increase? It is also unknown if larger animals compensate by increasing the proportion of fast-twitch (higher glycogen concentration) fibres, which can produce higher force per unit area than slow-twitch fibres. We investigated muscle fibre area and glycogen concentration in hindlimb muscles from varanids ranging from 105 g to 40,000 g. We found that fCSA increased with modest positive scaling against body mass (Mb0.197) among all our samples, and ∝Mb0.278 among a subset of our data consisting of never-frozen samples only. The proportion of low-glycogen fibres decreased significantly in some muscles but not others. We compared our results with the scaling of fCSA in different groups. Considering species means, fCSA scaled more steeply in invertebrates (∝Mb0.575), fish (∝Mb0.347) and other reptiles (∝Mb0.308) compared with varanids (∝Mb0.267), which had a slightly higher scaling exponent than birds (∝Mb0.134) and mammals (∝Mb0.122). This suggests that, while fCSA generally increases with body size, the extent of this scaling is taxon specific, and may relate to broad differences in locomotor function, metabolism and habitat between different clades.