Abstract <p>This paper develops a radial multiplier method based on a generalized Papkovich–Neuber representation with complex coefficients, reducing the original viscoelasticity equations to auxiliary potentials of the Helmholtz and Laplace equations. It is shown that system of homogeneous harmonic polynomials modified by a special system of radial functions defined by modified Bessel functions of half-integer index can be used as the basis system of potentials for analytically resolving the generalized Eshelby problem for spherical inclusions with a polynomial solution at infinity. This system of potentials is used to evaluate the effective dissipative and viscoelastic properties of dispersed composites with scale effects within the Eshelby–Christensen four-body spherical model. The generalized Eshelby problem for homogeneous or composite layered inclusions of spherical shape is understood to be a contact problem with a polynomial behavior of the solution at infinity. In the general case, it generalize the inclusion problem with a homogeneous field at infinity. It is assumed that the polynomial field at infinity is described by a system of harmonic polynomials.</p>