Abstract The paper discusses the possibility of predicting the dynamic behaviour, in terms of modal frequencies and loss factors, of sandwich beams with a constrained viscoelastic layer configuration. The problem is approached by the Rayleigh–Ritz method so that virtually any boundary condition can be dealt with by applying a single procedure. Simple polynomials are used as admissible functions and evidence of their good performance is given. The method is also suitable for the analysis of those arrangements where not only the viscoelastic material but also the external layers of the sandwich are damped.