On the example of a secluded acoustically subwavelength magnetic layer it is shown that the use of the tensor Green's function for solving elastostatic elastostatic boundary value problem allows us to obtain the structure of the magnon polarons spectrum in a form convenient for analysis, which is related to the formation of a special class of exchange-free of magnons - elastostatic spin waves and their associated resonance anomalies. In combination with a similar approach, previously developed for calculating the spectrum of dipole-exchange magnons, this method can be an alternative to the traditional way of analytical study of the dispersive features of the propa-gating magnetoacoustic waves in layered structures in conditions of simultaneous accounting of magnetoelastic, magneto-dipole and inhomogeneous exchange interactions.