In designing polymer composites, while their basic mechanical properties are seen as the primary interest for safety concern, their inherent damping values are seen as the secondary for human being comfort, safety and health. However, in today's advanced aerial and land vehicles, comport and health of passengers are as important as their safety. The aim of this work is to investigate the dynamic and also quasi-static behaviors of a glass fibre-reinforced polymer matrix composite, Hexply 913/33%/UD280, to be considered for structural as well as vibratory conditions. The specimens with different angles of fibre orientations (0, ± 10°, ± 20°, ± 35°, ± 45°, ± 55°, ± 70°, ± 80° and 90°) were manufactured from the composite prepreg and subjected to a vibrating beam test with the clamped-free boundary conditions. Two different methods, the half power bandwidth and the logarithmic free decay, were used to measure the damping values to be able to compare the results. A universal testing machine was used to obtain the stress-strain behaviors of the specimens. It has been revealed that the specimens with the ± 20°, ± 35° and ± 45° fibre orientations are able to produce high damping values with reasonable high maximum stresses. Especially the one with the ± 45 orientation is seen the best as it provides a high damping value and high strains to failure with an acceptable high stress. It is believed that such specimens are suitable for structural, vibratory and also impacted conditions, which is desired by many designers.