In this research, finite element and boundary element methods are coupled together to model the interaction of a piezoelectric ceramic working as an actuator with an elastic material. Piezoelectric-elastic material's interaction occurs in smart structures. This work is aimed at determining the actuation effects being transferred from the actuators to the host and the resulting overall structural response. To obtain the amount of these actuations, the system of the host structure and an actuator has been modeled by using coupled finite element boundary element method in frequency domain. The host structure, which is assumed as an isotropic elastic solid region is modeled as a half space. The piezoelectric ceramic region is modeled by the 3-D finite element method, while the elastic half space with boundary element method. Finite element model of piezoelectric ceramic and boundary element model of the elastic half space are coupled together at their interface such that the vibrations of the piezo-actuator induce vibrations in the elastic half space. A couple of examples are given to show the induced displacement field around the piezo-actuator on the surface of the elastic medium. The results show that high jump in magnitude of horizontal displacements at the corners of the actuator attached to the structure occurs, which is an indication of high stress concentration, of the shear stress type at the corners. This stress concentration sometimes causes complete debonding of the actuator from the base structure. By using the suggested BEM-FEM coupled model for actuators with different dimensions or material properties much useful information concerning the amount of actuation and load transfer can be obtained. The presented work is a step towards modeling of structural health monitoring systems.