<p>Solids in their noncrystalline phases become soft and exhibit viscoelastic behavior as a result of the application of mechanical forces. To understand the viscoelastic behavior of materials in their noncrystalline solid phases, a constitutive model is not available in the literature to the best of our knowledge. In some extent, continuum hyperelastic models can predict the behavior in macroscopic length scales. However, for very thin micro/nano-noncrystalline structures, these models may not be appropriate because they are not developed explicitly by considering molecular interactions. The novelty of the current work is the development of a constitutive relation to capture the viscoelastic response of noncrystalline solid phases of materials using molecular interactions. The noncrystalline solid phase is modeled by a large number of particles interacting with a hard-sphere intermolecular potential, so it becomes consistent with a continuum body. Using the existing continuum framework of viscoelasticity and Helmholtz free energy potential of noncrystalline phase of solids, Cauchy stress and corresponding evolution equation for viscoelastic stretch are derived. The current framework of constitutive modeling is also correlated with Maxwell’s representation of viscoelasticity, so it has versatile applicability on engineering materials. Current theoretical model is used to capture the viscoelasticity for uniaxial and equibiaxial extension, as well as pure shear. The experimental data available in the literature for uniaxial extension of polymeric and hydrogel are compared with the developed model. We achieve a very close agreement with the experimental results. The range of values of the parameter used in the energy dissipation function is determined from the convergence solution of the evolution equation for the equibiaxial extension. Because the current model considers microscopic molecular interactions, it can be utilized to predict the viscoelasticity of very thin micro/nano-noncrystalline structures.</p>