In the present paper damping of laminated composite shells is studied using the finite element method. The complex moduli of an orthotropic material are defined according to the elastic-viscoelastic correspondence principle. An eight-noded C degrees continuity, isoparametric quadrilateral element with five degrees of freedom per node (u, v, w, theta(x), theta(y)) is used to develop the complex eigenvalue problem based on complex moduli. A detailed parametric study is carried out to show the effects of fiber orientation, total number of layers, side to thickness ratio and curvature ratio on modal loss factors of laminated composite shells.