In the present paper, the finite element modeling of vibrating structures combined with piezoelectric materials and passive electric circuits (shunt circuits) is addressed, with emphasis placed on the analysis of two circuit topologies: resistive shunts and resistive-inductive shunts. The underlying formulation is first presented and then some numerical simulations using commercial finite element software are performed considering a free-free square plate and a complex piezoelectric vibrating beam accelerometer cell for which some target vibration modes must be attenuated. Results are presented and evaluated in terms of the vibration attenuation attained in each case analyzed.