The paper deals with the behaviour of structures with piezoceramic devices, loaded either with resistors or with inductors and resistors. Both the circuits can be represented by mechanical models: the first one is equivalent to viscoelastic models, whereas the second one is a single-degree-of-freedom (sdof) system, which is similar to a vibration absorber when added to the host structure. Since the device stiffness is frequency dependent, an iterative procedure ought to be adopted in order to get the eigenvalues, but completely acceptable numerical results can be obtained by an approximated technique, which uses the stiffness calculated at the desired angular frequency. Besides the mechanical models mentioned before can be profitably introduced into finite element codes (also commercially available), which allow one to get information on the modal parameters. For a structure with piezo devices shunted with resistive loads, if either the impulse response or the frequency response function is derived, the natural frequencies and damping ratios can be achieved by least-squares techniques without any bias, as demonstrated by studying a sdof system. The possibility provided by this approach has been shown by means of numerical examples carried out on beams, cantilevered and simply supported, modelled by finite element codes.