Laminated composite structures have considerably higher ability for the vibration damping than structures made of conventional materials. On the other hand the prediction of damping of composite structures is not straightforward due to their anisotropic behaviour. The anisotropic nature of composites brings the need for the accurate measurement of the damping parameters which are used for the prediction of the dynamic response. The present study concerns with the effectiveness and efficiency improvements of the inverse technique used for the identification of material damping coefficients of a laminated plate. The evaluated identification method combines numerical and experimental analyses. The effectiveness improvement of the method is realized by application of a vacuum chamber for dynamic tests in order to reduce the influence of the air damping on the identified damping coefficients. The efficiency improvement of the method is gained by proper definition of the minimization process with the use of the experiment design, the response surface methodology, and the strain energy approach for damping modelling. The Finite Element Modelling is realized using ABAQUS software and the minimization problem is defined using Isight environment.