The purpose of this study is to obtain the maximum loss factor of the embedded co-cure damping composite structure with the boundary condition of four edges clamped. To achieve this goal, the strain energy of each stress component is deduced using the Ritz method, and the loss factor of the structure is calculated. The present formulation is validated based on the results obtained using the finite element method. Finally, the law of loss factor variation with the change in structure thickness and layup angle is obtained. The results obtained show that the loss factor of the structure increases as the thickness of the structure increases; when the total thickness of the structure is constant, the loss factor increases first and then decreases, and there is an optimal value for the design; the optimal lay angle is pi/4.