Viscoelastic inserts have many useful applications in noise and vibration suppression of marine and aerospace structures. It is observed that the shape of such inserts play an important role in efficient absorption of vibration. Tapering of viscoelastic inserts may improve noise and vibration reduction in composite joints. Numerical simulations using FEM are carried out to find out the effect of the shape of inserts on vibration reduction and a combined FEM and Wave approach is developed to compare the inferences drawn from FEM analysis.