The concept of suppressing flexural and longitudinal wave motion in a free-free beam structure by use of embedded viscoelastic inserts is described. Taking the example of a simple aluminium beam it is shown that the shape of the insert in terms of the incident wave angle plays an important role in the efficient suppression of wave motion. The insert principle is then applied to a ‘top-hat’ stiffener section that forms part of a fibre-reinforced polymeric composite beam structure, typical of that used in the fabrication of marine structures. From this example it is shown that the use of specifically designed viscoelastic inserts can reduce flexural and longitudinal wave motion over a wide frequency range. The numerical studies are supported by experimental tests in the case of both the free-free beam and the more complex top-hat section structure.