This paper refers to the study of mechanical stress in superconducting toroidal and cylindrical coils, generated by high magnetic flux densities fields. First, it provides a brief overview of the theoretical elements related to superconducting devices and forces that occur. In the following sections numerical models are created in the Comsol Multiphysics software based on the finite element method. In order to compare the magnetic fields and mechanical stresses, similar dimensions are considered for the solenoid and torus. The numerical results obtained have an error of around 10 percent. The magnetic induction is with 7.3% higher in the toroidal coil, and the stress is 5.3% lower than in cylindrical coil. The numerical values are in a good agreement with the analytical values. The von Misses stress values are below the critical values of YBCO.