Behavior of a viscoelastic material under mechanical loading has been systematically investigated in this study in the scope of continuum mechanics, where the material was brought to a composite state by non-expansive fiber family considered as topological objects constituting only anisotropy. In this model no constraint was applied that would prevent realization of fiber reinforcement on molecular dimensions or on nano scale. Matrix part of the object has a viscoelastic anisotropy and, in addition to that, due to the fiber reinforcement, the object will wholly have an anisotropic structure.