The purpose of this work is to calculate the magnetic field induction distribution of a ring magnet and to investigate the force of its interaction with a cylindrical magnet for the possibility of using them as a magnetic spring. The calculation of the magnetic field induction distribution of cylindrical and ring magnets was performed on the basis of the method of virtual magnetic charges and by using the scalar magnetic potential. A map of the magnetic field of a ring magnet was constructed and its evolution was investigated depending on the geometrical parameters of the magnet. The existence of points of zero field on the axis of the magnet near its ends, where the direction of the field changes to the opposite, has been proved. An analytical expression for the induction of the magnetic field on the axis of the ring magnet was obtained, on the basis of which the dependence of the force of interaction of the magnet with a point magnetic dipole was calculated. Using the method of virtual magnetic charges and numerical integration, the force of interaction between tubular and cylindrical magnets of arbitrary sizes was calculated. The limits of applicability of the point magnetic dipole model for a cylindrical magnet are determined. Magnetic springs with different strength characteristics were studied. Such geometric dimensions of magnets were found, in which the force of their interaction in the working area does not depend on displacement. The results of the theoretical research carried out in this paper qualitatively and quantitatively agree with the known experimental data and allow to improve the strength characteristics of the magnetic spring. On the basis of the conducted research, a computer model was created in the Wolfram Mathematica system, showing a map of the magnetic field of a ring or tubular magnet of arbitrary size, as well as a computer model of a magnetic spring based on tubular and cylindrical magnets. The computer models are published as open source on the Wolfram Demonstration Project website and can be used both in the educational process and for the construction of magneto- mechanical devices.