The problem of the complex use of mineral raw materials is significant in the context of many industries. In the rare earth industry, in the context of limited traditional domestic reserves and dependence on imports of lanthanides, an unambiguous and comprehensive solution has not yet been developed. Promising areas include the involvement of technogenic raw materials in the industrial turnover. The present study examines the kinetics of the dissolution process of poorly soluble lanthanide compounds when changing the parameters of the system. The results obtained reflect the dependence of the degree of extraction of lanthanide on the following variable parameters of the system: temperature, concentration of the complexing agent, and intensity of mixing. On the basis of the experiment, the values of the activation energy and the reaction orders were calculated. The activation energy of the carbonate dissolution process, in kJ/mol, was as follows: 61.6 for cerium, 39.9 for neodymium, 45.4 for ytterbium. The apparent reaction orders of the carbonates are equal to one. The prospect of using the research results lies in the potential to create a mathematical model of the process of extracting a rare earth metal by the carbonate alkaline method. © 2021 by the authors. Licensee MDPI, Basel, Switzerland.