Glass fiber-reinforced composite materials are broadly adopted in automobile, aircraft, and naval applications due to their versatile mechanical characteristics. Structures made up of such composites are usually flexible and prone to vibrational behavior under the influence of dynamic loading. The possibility of structural failure increases at resonating vibration conditions under dynamic loadings. In this context, the composite structures should be designed in such a way that the resonance condition may be avoided. The various parameters, while fabricating the composite structures, such as fiber volume fraction, fiber orientation, dimensions, and in-elastic properties, are important for its dynamic behavior. These parameters may influence the modal characteristics of the composite structures. In this paper, the influence of fiber orientation on the natural frequencies and its related vibration modes of the glass fiber-reinforced epoxy composite material is studied experimentally. The vibrating modes of the composite plate are visualized by developing a Chladni setup. It is found that as the orientation of the fiber varies from 0° to 45°, the mode shapes also change. This shows that the fiber orientation has a major impact on the mode shapes of the structures made up of composites. Also, the influence of fiber orientation on the specific damping capacity of the composite material is studied in the present work. It is noticed that the specific damping capacity of the material increases as the fiber orientation varies from 0° to 45°.