Mechanical properties of living cells play an important role in helping to understand cell physiology and pathology. However, to ensure reliability, it is important to precisely define the experimental conditions of these mechanical test. In this study, viscoelastic properties of the outer layer (cytoplasm and membrane) were extracted using standard linear solid model. Finite element modeling of the two-layer cell was performed and the model was validated by experimental data. In the two-layer model, the effect of the radius of the nucleus and the location of the nucleus on the whole cell behavior were investigated. By increasing nucleus size, the whole cell properties follow the nucleus properties and the role of the nucleus becomes more dominant. By dislocating nucleus inside the cytoplasm, the cell behavior changes significantly and becomes more similar to that of nucleus properties. Similarly, changing the aspiration pressure and rate, impacts the observed behavior drastically. The results demonstrate that the location of the nucleus and the ratio of the radius of the cytoplasm to the radius of the nucleus can effectively influence the viscoelastic properties and mechanical behavior of the cell.