The present monograph is devoted to the theoretical and numerical study of the interaction of electromagnetic fields with deformable media. The models considered are based on different combination of the Lam´e and Maxwell equations. Several direct and associated with them inverse problems are studied. Then speaking about inverse problems, electromagnetic and elastic characteristics of a medium are the subject of reconstruction. Values of physical fields are connected through electromagnetoelastic interactions.

The authors consider the processes which are observed when seismic waves propagate in the Earth's crust. Variations of seismic and electromagnetic fields arising in this case are called *electromagnetoelastic waves*. The following types of electromagnetoelastic interactions are distinguished: interaction based on the *electrokinetic properties of a medium*, interaction based on the *piezoelectric properties of a medium* and interaction based on the *velocity effect*.

First, different statements of mathematical model of electromagnetoelastic interactions is described. Then the theoretical results of the numerical solution are discussed for various direct and inverse problems for the equations of electromagnetoelasticity.

Finally, the authors give some results of the numerical solutions of two inverse problems for the system of equations describing linear processes of interaction of electromagnetic and elastic waves.

Even if a complete review of the area is not exposed, rather wide range of problems and methods for their solution are discussed. This makes the monograph interesting and useful.