Free, out-of-plane vibration of a rotating beam with a non-linear, elastomeric constraint has been investigated. The elastomer is modelled as a parallel combination of spring and damper elements. The stiffness and damping parameters are evaluated by using previous experimental data. The linear analysis is performed by two techniques, one based on a power series expansion and the other based on the Rayleigh-Ritz principle. The results are found to be in excellent agreement. In the non-linear analysis, a numerical-perturbation technique is applied to determine the frequency-amplitude relationship. A parametric study revealing the influence of the non-linear constraint is presented. © 1999 Academic Press.