Owing to growing environmental awareness in green technology, the whole gamut of engineering sector has started shifting towards natural fibre-oriented materials from synthetic materials. The adequate dynamic stability and damping property are important design necessities in a polymer composite structure. Given this perspective, this paper discusses the formulation of distinct hybrid laminates with various weight ratios of jute- and linen-incorporated epoxy polymer and the influence of their weight ratios on the dynamic attributes. Dynamic mechanical thermal analysis is employed to quantify the viscoelastic attributes of the hybrid laminates. The natural frequency of cantilevered laminate beam is determined experimentally by free vibration analysis and the damping factor of the laminate beam is computed analytically by half power bandwidth technique. The cole-cole mapping analysis is made to understand the interfacial adhesion of the different laminates with hybrid configurations. The hybrid laminate with equal weight proportion of jute and linen is found to be optimal as it has exhibited maximum stiffness property and load bearing capability with high glass transition temperature. The influences of frequency on storage modulus and loss factor of the optimal hybrid laminate with respect to temperature are analysed. Several vibratory responses of the optimal hybrid laminate beam for different natural frequencies and damping factors are elicited and studied.