A three-dimensional anisotropic damage model, based on continuum damage mechanics, is presented capturing the damage induced anisotropy in the initially isotropic, viscoelastic (VE) solid. The second order tensor damage variable, conceived as an evolving structural tensor, is coupled with linear VE model at the finite as well as infinitesimal strains. A dissipation potential, based on a novel damage interaction tensor (fourth order tensor), is proposed from which the damage tensor evolution happens in an associative manner. The newly proposed model is numerically implemented as an implicit stress update algorithm, and the infinitesimal part of the formulation is validated against the available experimental results in the literature. A parametric study of the newly developed finite strain formulation is presented employing three different deformation histories demonstrating further the utility of the proposed anisotropic damage model. The successful experimental validation of the proposed model demonstrates its applicability and utility in the existing finite element codes. © 2022 Elsevier Ltd