A vibration analysis method is proposed for sandwich beams with a viscoelastic core. This method is applicable to the beams with arbitrary boundary conditions, intermediate supports and concentrated masses. The partial differential equation for bending of sandwich beams is transformed to an ordinary differential equation by means of Laplace transformation with respect to time. The effect of intermediate supports and concentrated masses is introduced into the equation by adding undetermined concentrated forces. Linear equations for the boundary values and the concentrated forces are derived from the differential equation by means of one-dimensional boundary element method. The harmonic response is calculated by solving the linear equations directly and eigenvalues are obtained by finding the points where the determinant of coefficient matrix vanishes using an iteration method.