A new component module (CM), called MLCE, has been implemented in the BEAM program. The CM takes into account the particular 'tongue-and-groove' design of the Elekta multi-leaf collimator (MLC) and the air gap between the leaves. The model was validated by two series of measurements and simulations. The first benchmarking series focuses on the interleaf leakage and the intraleaf transmission. The measurement showed a total transmission through the MLC of 1.42% of the open field dose. Two Monte Carlo (MC) simulations were made, the first with the new CM MLCE (inclusive of air gap) and the second with the CM MLCQ (exclusive of air gap), which is available in the BEAM distribution. When the air gap between the leaves was determined by varying the parameters of the leaf geometry within tolerance limits on the technical drawing, the total measured transmission of 1.42% was well reproduced by the CM MLCE. In contrast, MC simulations with MLCQ showed that the transmission through the MLC calculated without the interleaf leakage is only 44% of the total transmitted radiation. The relevance of the detailed MLC modelling was demonstrated also by studying the 'adjacent' tongue-and-groove effect, where two adjacent (not opposing) leaves are complementary, opened or closed. The two complementary leaf settings were simulated both with the CM MLCE and MLCQ. A comparison with measurements was made. In regions covered by two or more leaves, the dose increased by 14% for two leaves and by 40% for more than two leaves when the interleaf leakage was included in the transmission. The tongue-and-groove effect was perfectly reproduced by the MLCE module.