In the paper the natural frequencies and modal loss factors of a three-layered rectangular cantilever plate with high-modulus composite face layers and a viscoelastic mid-layer are discussed. Two analysis approaches are considered, the Ritz method and the finite element method. The Ritz analysis is based on an appropriate 2-D plate model. Algebraic polynomials are used which satisfy the necessary geometric boundary conditions. The discretized eigenvalue problem is then solved for complex eigenvalues, from which damped frequencies and modal loss factors are extracted. Both frequencies and loss factors are shown to converge with an increasing number of the polynomials used. Apart from the Ritz method, frequencies and modal loss factors are calculated by the finite element method based on the so-called strain energy method. Comparison between the two approaches is then given.