Relevance of the research topic. During operation rubber-cord couplings with a toroidal shell form may fail. For the period from 2019 to 2023 (5 years) such failures amounted to more than 58 cases. According to a visual inspection of a large number of failed rubber-cord couplings, it was found that the cause of failure was a rupture of the side surface. The aim of this scientific article is to determine the forces and moments acting on the rubber-cord coupling, as well as the displacements of the shafts connected by the rubber-cord coupling in axial, radial and angular deflections. To determine the properties of the material, a series of single tensile and cyclic tests of fragments of rubber-cord couplings were carried out. Based on the test results, a mathematical model of the material was determined. In the environment of the FEM software, the test results were compared with models of elastomeric materials and the most suitable model of elastomeric material that most accurately corresponded to the test results was selected. The calculated forces and torque effects were simulated, and the effects of radial, axial and angular deflection and measured coupling deflections were simulated. The purpose of modelling is to identify dangerous operating modes and dangerous forms of the rubber-cord couplings loading during operation.