We investigate the two basic internal BVPs related to the linear theory of viscoelasticity for Kelvin-Voigt materials with voids by means of the potential theory. By using an indirect boundary integral method, we represent the solution of the first (second) BVP of steady vibrations in terms of a simple (double) layer elastopotential. The representations achieved are different from the previously known ones. Our approach hinges on the theory of reducible operators and on the theory of differential forms.