Finite element solutions using a general purpose computer program NASTRAN for damped structures are formulated and presented. Continuously and discontinuously constrained layer damped configurations are the two classes of structures considered. The former is the three‐layered sandwich composite made up of two thin elastic layers with a viscoelastic damping core between them, while the latter is the damped composite made of a thin‐walled elastic structure having a finite number of mass segments or elastic segments adhered to it by a viscoelastic material. The dependence on frequency and temperature of the dynamic properties of the viscoelastic materials is taken into consideration. Typical numerical solutions of transverse driving point mechanical impedances as well the transfer impedances of three‐layered sandwich damped structural elements such as beam, ring, plate, and discontinuously constrained damped ring are presented and discussed. These solutions compare very well with experimental data and available theoretical results obtained by other analytical methods.