This paper describes a numerical method for the solution to the inverse problem for the equations of electromagnetoelasticity. We consider the case when electromagnetic waves are generated by elastic deformations. At the same time, we neglect the reverse influence of the electromagnetic field on the elastic oscillations.

We focus our attention on one of the simplest versions of the system of the equations of electromagnetoelasticity which, at the same time, preserves the basic properties of more adequate model. The solution to the inverse problem (the unknown elastic and electromagnetic medium parameters) is sought by means of minimization of the data misfit functionals which are the mean square deviations of the registered fields from the fields calculated for some ``test" medium models.

Results of numerical experiments are given to illustrate the efficiency of the method.

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