<p>The stretched exponent Kohlrausch-Williams-Watts (KWW) equation, which is to some extent equivalent to the generalized Maxwell viscoelastic model, is widely employed for analyzing relaxation dynamics and nonelastic deformation of amorphous solids. However, it cannot reveal the underlying physical mechanisms of anelasticity. In this study, based on the potential atomic mechanisms of amorphous solids within a strain field and the traditional viscoelastic model, we introduced a physical-mechanical model involving hierarchically constrained atomic motion around defect sites. This model deduces that fast atoms move first, subsequently facilitating more complex atomic rearrangements under thermomechanical loading. These atom movement mechanisms are involved in the evolution of deformation units, such as shear transformation zones (STZs). Initially, anelasticity is associated with isolated STZs because of back stress arising from the matrix. Subsequently, the percolation of STZ by the motion of atoms owing to STZ interactions leads to irreversible deformation. The model was validated by describing the elastic, anelastic, and plastic components of stress relaxation in a La₆₀Ni₁₅Al₂₅ metallic glass. Furthermore, as STZs are connected to <i>α</i> and <i>β</i> relaxation processes, the model can be used for parameter description and component analysis of dynamic stress relaxation. The current study supplements the traditional flow defect model, providing insights into the deformation mechanisms of metallic glasses from the perspective of viscoelastic mechanics and their correlation with dynamic relaxation processes.</p>