This study describes the viscoelastic properties of a refined cellular-tensegrity model composed of six rigid bars connected to a continuous network of 24 viscoelastic pre-stretched cables (Voigt bodies) in order to analyse the role of the cytoskeleton spatial rearrangement on the viscoelastic response of living adherent cells. This structural contribution was determined from the relationships between the global viscoelastic properties of the tensegrity model, i.e., normalized viscosity modulus (eta(*)), normalized elasticity modulus (E(*)), and the physical properties of the constitutive elements, i.e., their normalized length (L(*)) and normalized initial internal tension (T(*)). We used a numerical method to simulate the deformation of the structure in response to different types of loading, while varying by several orders of magnitude L(*) and T(*). The numerical results obtained reveal that eta(*) remains almost independent of changes in T(*) (eta(*) proportional, variant T(*+0.1)), whereas E(*) increases with approximately the square root of the internal tension T(*) (from E(*) proportional, variant T(*+0.3) to E(*) proportional, variant T(*+0.7)). Moreover, structural viscosity eta(*) and elasticity E(*) are both inversely proportional to the square of the size of the structure (eta(*) proportional, variant L(*-2) and E(*) proportional, variant L(*-2)). These structural properties appear consistent with cytoskeleton (CSK) mechanical properties measured experimentally by various methods which are specific to the CSK micromanipulation in living adherent cells. Present results suggest, for the first time, that the effect of structural rearrangement of CSK elements on global CSK behavior is characterized by a faster cellular mechanical response relatively to the CSK element response, which thus contributes to the solidification process observed in adherent cells. In extending to the viscoelastic properties the analysis of the mechanical response of the cellular 30-element tensegrity model, the present study contributes to the understanding of recent results on the cellular-dynamic response and allows to reunify the scattered data reported for the viscoelastic properties of living adherent cells.