Abstract The viscoelastic properties of the living cells are for quantifying the biomechanical effects of drug treatment, diseases and aging. Nanoindentation techniques have proven effective to characterize the viscoelastic properties of living cells. However, most studies utilized the Hertz contact model and assumed the Heaviside step loading, which does not represent real tests. Therefore, new mathematical models have been developed to determine the viscoelastic properties of the cells for nanoindentation tests. Finite element method was used to determine the empirical correction parameter in the mathematical model to account for large deformation, in which case the combined effect of finite lateral and vertical dimensions of the cell is essential. The viscoelastic integral operator was used to account for the realistic deformation rate. The predictive model captures the mechanical responses of the cells observed from previous experimental study. This work has demonstrated that the new model consistently predicts viscoelastic properties for both ramping and stress relaxation periods, which cannot be achieved by the commonly used models. Utilization of this new model can enrich the experimental cell mechanics in interpretation of nanoindentation of cells.