A method of analysis for the forced vibration of a beam with viscoelastic boundary supports is proposed based on complex normal mode analysis. The viscoelastic support regions are first described in terms of equivalent complex stiffness coefficients, and then using the complex modes of the beam system with complex stiffness at the boundary points, the equations of motion are completely uncoupled. The modal equation has precisely the same form as the equation of a structurally damped single-degree-of-freedom system. Effects of the viscoelastic supports on the forced vibration response are discussed as an example. (C) 1998 Academic Press Limited.