It is generally accepted that the human neutrophil can be mechanically represented as a droplet of polymeric fluid enclosed by some sort of thin slippery viscoelastic cortex. Many questions remain however about the detailed rheology and chemistry of the interior fluid and the cortex. To address these quantitative issues, we have used a finite element method to simulate the dynamics of neutrophils during micropipet aspiration using various plausible assumptions. The results were then systematically compared with aspiration experiments conducted at eight different combinations of pipet size and pressure. Models in which the cytoplasm was represented by a simple Newtonian fluid (i.e., models without shear thinning) were grossly incapable of accounting for the effects of pressure on the general time scale of neutrophil aspiration. Likewise, models in which the cortex was purely elastic (i.e., models without surface viscosity) were unable to explain the effects of pipet size on the general aspiration rate. Such models also failed to explain the rapid acceleration of the aspiration rate during the final phase of aspiration nor could they account for the geometry of the neutrophil during various phases of aspiration. Thus, our results indicate that a minimal mechanical model of the neutrophil needs to incorporate both shear thinning and surface viscosity to remain valid over a reasonable range of conditions. At low shear rates, the surface dilatation viscosity of the neutrophil was found to be on the order of 100 poise-cm, whereas the viscosity of the interior cytoplasm was on the order of 1000 poise. Both the surface viscosity and the interior viscosity seem to decrease in a similar fashion when the shear rate exceeds approximately 0.05 s(-1). Unfortunately, even models with both surface viscosity and shear thinning studied are still not sufficient to fully explain all the features of neutrophil aspiration. In particular, the very high rate of aspiration during the initial moments after ramping of pressure remains mysterious.