The analysis of circular plates with a constrained viscoelastic damping layer treatment is carried out in this paper. A finite annular element based on individual layer theory is developed for this purpose. The influence of core-to-facing thickness ratio and shear modulus of the core on the frequencies and loss factors of a circular plate with isotropic facing is analysed in this paper. The study is conducted for three boundary conditions: (i) clamped at both edges, (ii) simply supported at both the edges and (iii) clamped free edges. © 1993.