Moults characterise insect growth trajectories, typically following a consistent pattern known as Dyar's rule; proportional size increments remain constant across inter-instar moults. Empirical work suggests that oxygen limitation triggers moulting. The insect respiratory system, and its oxygen supply capacity, grows primarily at moults. It is hypothesized that the oxygen demand increases with increasing body mass, eventually meeting the oxygen supply capacity at an instar-specific critical mass where moulting is triggered. Deriving from this hypothesis, we develop a novel mathematical model for moulting and growth in insect larvae. Our mechanistic model has great success in predicting moulting sizes in four butterfly species, indirectly supporting a size-dependent mechanism underlying moulting. The results demonstrate that an oxygen-dependent induction of moulting mechanism would be sufficient to explain moulting sizes in the study species. Model predictions deviated slightly from Dyar's rule, the deviations being typically negligible within the present data range. The developmental decisions (e.g. moulting) made by growing larvae significantly affect age and size at maturity, which has important life history implications. The successful modelling of moulting presented here provides a novel framework for the development of realistic insect growth models, which are required for a better understanding of life history evolution.