The author considers the principles of construction, the structure of a software and mathematical model of the Earth`s crust’s movements. It is designed to ensure the maintenance of the state reference frame relevance, the establishment and maintenance of the national reference systems’ relationship with international ones for the Russian Federation’s territory. The software implementation should include mathematical models of geodynamic processes for the state’s territory and algorithms for taking them into account for determining coordinates in a given frame of reference. The author presents a general scheme of the above-mentioned model, which consists of several layers. The first base layer containing a model of the tectonic blocks movement and complemented by those of local solutions. Four stages of the model are described. The mathematical basis and software tools are considered. Employing of the first solution of the crust movements software-mathematical model for the Russian Federation’s territory is presented. It is based on that of lithospheric plates motion NNR-MORVEL56. The results of determining the Earth`s crust’s points velocities are compared with those of the Plate Motion Calculator. The coincidence of the calculated values up to hundredths of a millimeter is noted