The presented method is based on the model of an axially magnetized cylinder. The power characteristics of interacting cylinders and / or coils are equivalent if their surface currents are equal. The magnetic system can be composed of cylinders and/or coils. The mutual inductances of the coils follow from the mutual energy of the cylinders, determined through the 3D fields. The fields are calculated using Bessel functions. The features of numerical calculations using the Bessel functions and elliptic integrals are discussed. It is shown that, in calculations using the Bessel functions, there are field oscillations over the end surfaces of the cylinder and local discontinuities of the force graphs appear.