This paper presents preliminary results from an analysis of the damping properties of a composite isogrid panel with an embedded viscoelastic layer by means of a finite element method (FEM) implementation of the modal strain energy method (MSE). Modal analysis shows that significant shear deformation occurs in the region between the ribs and the face skin because of the stiffness mismatch between the two. Since the performance of a viscoelastic polymer damping material is optimized by subjecting the material to shear deformation, such damping materials can be placed at the interface between the ribs and the skin in order to significantly improve the damping properties of composite isogrid structures. It is shown that the shear strain energy density (energy per volume) near the edges of the panel in the damping layer is much higher than that at the center area for the first free-free vibration mode. As a first attempt at improvement of damping, the effect of using different amounts of damping materials on the loss factor of the isogrid panel is also studied.