The paper presents a study of the inverse problem of identification of mechanical and piezoelectric characteristics of functionally graded piezoelectric polymer rod. The defining relations for the electrodynamics piezo-polymer are formulated based on the conception of complex modules, similar to the model of viscoelasticity. With this approach two types of load are considered: mechanical – through the application of the load to the end of the rod without applying electrical current in the circuit and electrical – by applying a potential difference at the ends of the rod. One of the ends of the rod considered rigidly clamped. Thus, from two experiments able to get two kinds of additional information for solving the inverse problem. It is the displacement of the rod and the potential of electric field. These characteristics are measured on the free end of the rod in a certain frequency range. For convenience of further studies dimensionless parameters and variables were introduced. Due to a significant nonlinearity of the inverse problem we have built a special iterative process of solving, which based on a combination of linearization method and Tikhonov regularization. At each step of the iterative process at first stage we solve the direct problem of determining the functions of displacement and electric field potential in the rod. Solution of the direct problem performed in two ways – by using Runge-Kutta-Felberg method and by using Fredholm integral equations of the 2nd kind. On the second stage the modifications to unknown functions are isolated from the constructed system of Fredholm integral equations of the 1st kind. To solve this system, due to incorrect handling procedures method of regularization A.N.Tikhonov is used. The results of computational experiments of identification of inhomogeneous mechanical and piezoelectric characteristics of the functionally graded piezo-polymer rod are presented. Experiments have shown that unknown functions are possible to identify with an error not exceeding 6-8%, which confirms the effectiveness of the developed approach.