A response of systems with different damping models to transient excitations is studied using the finite element method. For this purpose an e.cient method using fast Fourier transform has been developed. This method is based on the trigonometrical representation of the input signals and matrix of the transfer functions. As an example, systems with viscous and viscoelastic, structural and external damping are examined. Two forms of viscous damping are available in the present implementation: Raleigh damping and element damping. The viscoelastic material behaviour is represented by the complex modulus model. The present implementation gives the possibility to preserve exactly the frequency dependence of the storage and loss moduli of viscoelastic materials. Logarithmic decrements are determined using the steady-state vibrations of systems to characterize their damping properties. Test problems and numerical examples are given to demonstrate the validity and application of the approach suggested in this paper.