This paper is concerned with the development of a computational basis for modeling time-dependent effects in a finite or an infinite viscoelastic medium containing multiple circular cavities. A two-dimensional model for a suitably oriented plane section through a porous polymeric material is adopted. The solution of the problem is based on the use of the correspondence principle. The governing equation for this problem in the Laplace domain is a complex hypersingular boundary integral equation written in terms of the unknown transformed displacements at the boundaries of the holes. The method allows to accurately calculate the viscoelastic fields anywhere within the material. The effective viscoelastic properties of an equivalent homogeneous material can then be found directly from the corresponding constitutive equations for the average field values.