The largest human blood cells—the red cells (erythrocytes) and white cells (leukocytes)—must undergo a significant amount of deformation as they squeeze through the smallest vessels of the circulation and the small openings between bone, vessel and tissue. This ability to deform in response to external forces shows that cells exhibit material behavior and behave as either elastic solids or viscous liquids. The question then is “how can we measure the deformation and flow of something as small as a blood cell and what kinds of constitutive equations describe cellular deformation”? In this paper the use of the micropipet to measure red cell and white cell, especially neutrophil, deformation will be described and the viscoelastic models used to describe the deformation behavior of red cell membrane and neutrophil cytoplasm will be discussed. Values for the elasticities of a red cell membrane subjected to shear, area expansion and bending will be given. The viscosity of red cell membrane in shear will also be discussed. Finally, the cortical tension of the neutrophil and the Newtonian and Maxwell models used to characterize its apparent viscosity will be discussed even though neither is wholly successful in describing the viscous behavior of the neutrophil. Thus, alternate models will be suggested.