This paper presents an analysis of conical shells with a constrained viscoelastic damping treatment. A finite element based on a discrete layer theory is developed for the purpose. The effects of core-to-facing thickness ratio, slant length and semi vertex angle of the cone on the frequencies and loss factors of conical shells with isotropic facings are investigated for three boundary conditions: clamped at both ends, simply supported at both ends and clamped at the small end. The effect of the shear parameter on the frequency and loss factor is also presented. © 1993.