An effective method based on linearization of the Landau-Lifshitz equation has been developed to determine normal magnetization oscillation modes in a discrete model of a condensed medium. The possibility to calculate microwave absorption spectra for ferromagnetic specimens of any shape is shown.The fundamental equation that describes the dynamics of a magnetic system under the action of external constant and variable magnetic fields is the Landau-Lifshitz nonlinear differential equation. For a discretized model of an inhomogeneous medium, it is necessary to solve a system of connected nonlinear differential equations. To solve systems of this type, numerical integration based on an algorithm similar to the Runge-Kutta algorithm is widely used [1]. The main advantage of this approach is the possibility to predict the evolution of a magnetic system, starting from the initial distribution of magnetic moments in the discrete model. The main disadvantages of this type of algorithm are substantial computational burden and the inconstancy of the magnetic moment vector in discrete elements in iterative calculations, which in fact gives no way of investigating systems that consist of a large number of elements. Therefore, undoubtedly, the search for new approaches and algorithms which would allow one to solve complicated problems of this type is of importance and urgency in modern physics. The potentialities of multilayer magnetic structures used in microelectronic devices also promote the extension of related research works.In recent years, to study microdiscrete models of complicated magnetic structures, approaches have been developed that have been actively used in optics [2][3][4]. They are based on a description of the motion of magnetic moments as the sum of the natural oscillations of the normal magnetic modes for the overall system. In this paper, the idea described elsewhere [2] is developed as applied to a discrete model [5], which has shown rather high efficiency.A ferromagnetic is represented as a discrete medium consisting of N identical (of volume V 0 ) dipoles μ (i) (i = 1, 2, …, N) that, having a constant saturation magnetization M s , fill uniformly the whole of the body. Denoting the direction of the ith dipole by M (i) , we write an expression for the free energy density of the system, F, taking into account the Zeeman energy, the exchange and dipole interaction energies, and the energy of uniaxial magnetic anisotropy: