Commercial TPSs typically model the tongue-and-groove (TG) by extending the projections of the leaf sides by a certain constant width. However, this model may produce discrepancies of as much as 7%-10% in the calculated average doses, especially for the High Definition multi-leaf collimator (MLC) (Hernandez et al 2017 Phys. Med. Biol. 62 6688-707). The purpose of the present study is to introduce and validate a new method for modelling the TG that uses a non constant TG width. We provide the theoretical background and a detailed methodology to determine the optimal shape of this TG width from measurements and we fit an empirical function to the TG width that depended on two parameters [Formula: see text] and [Formula: see text]. Parameter [Formula: see text] represents the TG width and [Formula: see text] introduces a curvature correction in the width near the leaf tip end. The new TG model was implemented in MATLAB and when the curvature correction was zero ([Formula: see text]) it caused the same discrepancies as the constant width model used by the Eclipse TPS. On the other hand, when the experimentally determined [Formula: see text] was used the new model's calculations were in close agreement with measurements, with all differences in average doses [Formula: see text]1%. Additionally, film dosimetry was used to successfully validate the potential of the new TG model to recreate the fine spatial details associated to TG effects. We also showed that the parameters [Formula: see text], [Formula: see text] depend solely on the MLC design by evaluating three different linear accelerators for each MLC model considered, namely Varian's High Definition and Millennium120 MLCs. In conclusion, a new method was presented that greatly improves the TG modelling. The present method can be easily implemented in commercial TPSs and has the potential to further increase their accuracy, especially for MLCs with rounded leaf ends.