The response of structures made from viscoelastic materials to transient excitations is studied using the finite element method. The viscoelastic material behaviour is represented by the complex modulus model. An efficient 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. The present implementation gives the possibility to preserve exactly the frequency dependence of the storage and loss moduli of materials. On this reason this time‐domain representation is a mathematically correct way to avoid the non‐causal effect. Test problems and numerical examples are given to demonstrate the validity and effectiveness of the approach suggested in this paper. Copyright © 1999 John Wiley & Sons, Ltd.