A three-layer Newtonian model is investigated using a combined Eulerian-Lagrangian computational method to describe the dynamic behaviour of leukocytes. The model, composed of a cell membrane (outer layer), cytoplasm (middle layer) and nucleus (inner layer), can better describe the recovery characteristics because large viscosity and capillarity differences between layers are considered, and both Newtonian and seemingly non-Newtonian behaviours reported in the literature can be reproduced. It is found that, to describe adequately the various rheological characteristics of leukocytes, the presence of the highly viscous nucleus and its deformation/recovery, as well as the surface energy stored in the fluid interfaces, are critical. Photographs from pipette experiments using a fluorescent technique confirm the theoretical finding of the important role played by the nucleus in cell deformation.