The mathematical description of the hydrogen desorption process from liquid aluminium and its alloys in the bubbling process was presented. The mathematical model based on the equation for the mass transfer coefficient and dimensionless number of the hydrogen concentration introduced by Sigworth and Engh is presented. This mathematical modelling was carried out for the continuous reactor under the atmospheric pressure. Also, the selection of main thermodynamic and kinetic parameters, that are essential to modelling calculations, was done. Among the most important parameters there are: the hydrogen solubility in aluminium and its alloys, the interfacial contact area in the system: liquid metals - the bubble of refining gas (this area can be determined using estimated values of the bubble rise velocity and the bubble diameter), and the mass transfer coefficient. The hydrogen solubility in aluminium alloys can be described basing on the activity coefficient calculated from Wagner's interaction parameters. This model and correctness of assumptions, which were made, were verified. The comparison of the calculated hydrogen concentration with the industrial data for AK-64 alloy refining in a continuous reactor under the atmospheric pressure was carried out. The simulation of the refining process under vacuum based on the experimental data for AK-64 alloy under atmospheric pressure was done.