Using the example of a solitary acoustically subwave„length magnetic layer, it is shown that employing the tensor Green's function to solve the elastostatic boundary value problem makes it possible to obtain the spectrum structure of magnon polarons in a form convenient for analysis, associated with the formation of a special class of exchange-free magnons — elastostatic spin waves and resonance anomalies accompanying them. In combination with a similar approach previously developed for calculating the spectrum of dipole-exchange magnons, the method can be an alternative to the traditional method of studying analytically the dispersion features of magnetoacoustic waves propagating in layered structures under conditions of simultaneous magnetoelastic, magnetodipole, and inhomogeneous exchange interactions.