<p>Numerical method for solving the problems of nonstationary vibrations for structural members made of electroelastic functionally graded material is presented taking into account electromechanical losses and interaction with the acoustic medium. Universal numerical approach is used for studying the vibrations of plane layers, cylinders, and spheres. It is based on finite-difference expressions. To take into account the dissipative characteristics of the material, the Kelvin–Voigt viscoelasticity model is used for the case of electroelasticity. Similar to complex moduli, the mechanical, dielectric, and piezoelectric damping coefficients are introduced to account for mechanical and electrical losses. Numerical studies of the behavior of functionally inhomogeneous cylinders and spheres under the action of nonstationary electrical load have shown that mechanical losses have the greatest effect on the damping of vibrations. It is concluded that taking into account energy dissipation according to the viscoelastic Kelvin–Voigt model with experimentally substantiated damping coefficients allows modeling the vibrations of piezoelectric elements with sufficient accuracy. The dependence of the logarithmic decrements of vibrations on the polymer fraction and the geometric dimensions of the cylinder is studied. The damping of vibrations of a piezoelectric sphere immersed in the fluid under electrical load of a step-like profile is analyzed. It is established that the damping of vibrations occurs in this case more than ten times faster than when accounting for internal mechanical losses without the acoustic medium.</p>