Recently, the Subcellular Element Model (SEM) has been introduced, primarily to compute the dynamics of large numbers of three-dimensional deformable cells in multicellular systems. Within this model framework, each cell is represented by a collection of elastically coupled elements, interacting with one another via short-range potentials, and dynamically updated using over-damped Langevin dynamics. The SEM can also be used to represent a single cell in more detail, by using a larger number of subcellular elements exclusively identified with that cell. We have tested whether, in this context, the SEM yields viscoelastic properties consistent with those measured on single living cells. Employing virtual methods of bulk rheology and microrheology we find that the SEM successfully captures many cellular rheological properties at intermediate time scales and moderate strains, including weak power law rheology. In its simplest guise, the SEM cannot describe long-time/large-strain cell responses. Capturing these cellular properties requires extensions of the SEM which incorporate active cytoskeletal rearrangement. Such extensions will be the subject of a future publication.