The problem of characteristics identification of inhomogeneous viscoelastic rods at bending vibration is considered. The method of construction of the functional relations linking required and set functions is presented. The solution is constructed by means of the iterative process, combining on each step a solution of a direct problem and corrections definition on the base of solution of an integral equation of Fredholm of 1st kind with the smooth kernel. The results of numerical experiments on definition of inhomogeneous characteristics of viscoelastic rods are presented.