A general method for constructing a material damping matrix in dynamical systems based on viscoelastic assumptions is presented. A generalization of the classical lamination theory, in particular, the consideration of viscoelasticity in the constitutive relation is considered. The discretized equations of motion for a laminated anisotropic viscoelastic plate using the finite-element method are derived. The mass, damping and stiffness matrices are completely defined and arise consistently in the formulation of motion equations. The technique is illustrated by calculating the mass, damping and stiffness matrices of a graphite-reinforced epoxy shell element. The eigenvalues are then calculated for the resulting eigenproblem.