ABSTRACT: The paper considers the problems of natural vibrations of viscoelastic plates with different boundary conditions in magnetic fields. The aim of the work is to study the oscillations of thin-walled structural elements in a magnetic field: to calculate the spectra of natural frequencies and vibration damping coefficients of rectangular viscoelastic plates with different conditions for fixing the edges, as well as to study the effect of the transverse and longitudinal magnetic field induction on the values of natural frequencies and damping coefficients, as well as their distribution. The validity and reliability of the results of the work is ensured by the correct statement of the problems, the use of applied mathematics metathemes, modern software and the comparison of the results with the results given in scientific publications. For calculations, mathematical packages MATLAB, software environment MAPLE-18 are used. The paper first obtained analytical solutions for calculating the complex vibration frequencies of viscoelastic plates with a different combination of boundary conditions. A numerical analysis of the oscillations of rectangular viscoelastic plates with different conditions for fixing the edges is carried out, the influence of the transverse and longitudinal magnetic fields on the spectrum of complex frequencies is studied. New effects that the magnetic field exerts on the distribution of natural frequencies and the damping coefficient of the plate element structures are found.