The article presents the methodology for finding material damping capacity at higher frequency and at relatively lower amplitudes. The Lamb wave dispersion theory and loss less finite element model is used to find the damping capacity of composite materials. The research has been focused on high frequency applications materials. The method was implemented on carbon fiber reinforced polymer (CFRP) and glass fiber reinforced polymer (GFRP) plates. The Lamb waves were generated using ultrasonic pulse generator setup. The hybrid method has been explored in this article and the results have been compared with bandwidth methods available in the literature.