In this study, transient dynamic response of filament wound cylindrical composites subjected to shear tractions is investigated. The cylindrical composite consists of n different layers. Layers with different winding angles are modelled as orthotropic, homogeneous and linearly elastic materials. The cylindrical composite is subjected to uniform time dependent shear tractions at its inner surface and the outer surface is free of surface tractions. The composite body is assumed to be initially at rest. The governing field equations of anisotropic elasticity are applied to each layer and the solutions are required to satisfy the interface conditions, the boundary conditions, and quiescent initial conditions. Method of characteristics is employed to obtain the solution. The numerical results are displayed in curves denoting the variations of the shear stresses with time at different locations along the thickness of the cylindrical composite. These curves reveal clearly the effects of reflections and refractions at the boundaries and the interfaces of the layers, the effects of geometric dispersion, and the effects of fiber orientation angle.