Industry represents a fundamental component of modern society, with the generation of massive amounts of industrial waste being the inevitable result of development activities in recent years. Red mud is an industrial waste generated during alumina production using the Bayer process of refining bauxite ore. It is a highly alkaline waste due to the incomplete removal of NaOH. There are several opinions in both the literature and legislation on the hazards of red mud. According to European and national legislation, this mud is not on the list of hazardous wastes; however, if the list of criteria are taken into account, it can be considered as hazardous. The complex processing of red mud is cost-effective because it contains elements such as iron, manganese, sodium, calcium, magnesium, zinc, strontium, lead, copper, cadmium, bismuth, barium and rare earths, especially scandium. Therefore, the selection of an extraction method depends on the form in which the element is present in solution. Extraction is one of the prospective separation and concentration methods. In this study, we evaluated the kinetic modelling of the solid–liquid acid extraction process of predominantly scandium as well as other elements present in red mud. Therefore, three acids (HCl, HNO3 and H2SO4) at different concentrations (10, 20 and 30%) were targeted for the extraction of Sc(III) from solid red mud. Specific parameters of the kinetics of the extraction process were studied, namely the solid:liquid ratio, initial acid concentration, contact time and temperature. The extraction kinetics of Sc(III) with acids was evaluated using first- and second-order kinetic models, involving kinetic parameters, rate constants, saturation concentration and activation energy. The second-order kinetic model was able to describe the mechanism of Sc(III) extraction from red mud. In addition, this study provides an overview on the mechanism of mass transfer involved in the acid extraction process of Sc(III), thereby enabling the design, optimization and control of large-scale processes for red mud recovery.