As the French nuclear glasses used to confine the long-lived radionuclides are intended to be stored definitively in a deep geological repository, it is important to predict the alteration rate when being in contact with underground water. This alteration rate is directly connected to the release of the radioelements into the environment. For the development of a predictive model, the first step is to determine the preponderant elementary mechanisms explaining the glass alteration because they could constitute the building blocks. More and more sophisticated Monte Carlo algorithms have been developed in previous years to try to determine these elementary mechanisms. This presentation will propose a history of these developments from the very first model proposed by M. Aertsens until the one we are currently developing to better and better approach the real case. The first attempt to simulate nuclear glass alteration using a Monte Carlo approach is due by M. Aertsens from Mol in Belgium. An ordered SiO2-Na2O network in contact with water was built to simulate the glass alteration and a set of probabilities were introduced to represent the Si release in solution and the Na+-H+ exchange mechanisms. But this method was limited because of a too-long computational time. Then a refined algorithm was developed at CEA Marcoule [1,2]. The glass composition considered was more complex (up to five oxides SiO2-B2O3-Na2O-CaO-ZrO2) and the glass structure was still represented by an ordered network in contact with water. A larger set of probabilities was used to simulate the glass former hydrolysis (Si, Al). One Si or one Al ion in contact with water was released in solution with a probability depending on the local degree of polymerization of its site. The B atoms were immediately released in the solution when in contact with water. Using this more sophisticated algorithm, it has been possible to reproduce with good agreement some experimental results, like the B release amplitude in SiO2-B2O3-Na2O glasses at different S/V ratios, or the ZrO2 strengthening effect. Later, S. Kerisit at PNNL [3] continued to improve the Monte Carlo method first by adding Al2O3 to the glass composition, then by considering the boroxols rings effect. He developed his own code independently of the CEA work. He observed a non-linear impact of Al2O3 on the glass alteration and an acceleration of the glass alteration with the number of boroxol rings. CEA and PNNL codes were later compared successfully during A. Jan’s thesis [3]. One of the main objectives of this thesis was to use these Monte Carlo codes to try to reproduce the alteration layer depth increase after irradiation by heavy ions. But it has not been possible to trigger the Monte Carlo probabilities to reproduce these radiation effects. From this work, it has been concluded that other important elementary mechanisms were still missing. For this reason, a refined Monte Carlo algorithm is currently in development. The main difference with the previous CEA and PNNL codes is the possibility for water to diffuse inside the glass (this was not considered previously) and the possibility to represent the alteration layer ripening. We hope that thanks to these new options, it will be possible in the future to represent more precisely the radiation effects on the alteration layer depth. The first results obtained with this refined Monte Carlo method will be presented for a series of SiO2-B2O3-Al2O3-Na2O glasses. The figure represents an example of an alteration layer simulated by this algorithm.