Red cells which adhere to a surface in a parallel plate flow channel are stretched when acted on by a fluid shear stress. Three types of stretching are studied: whole cell stretching, the stretching of a red cell evagination, and tether (long, thin membrane process) stretching. In addition, the stretching of a large scale model cell attached to a surface is studied in a Couette flow channel. The results indicate that the uniaxial stretching of red cell membrane can be described by a linear stress-strain relationship. Simple theories developed from free body diagrams permit the calculation of a value for the modulus of elasticity of cell membrane in each of the three experiments. In all cases the value for the modulus is on the order of 10(4) dyn/cm(2) for an assumed membrane thickness of 0.01 mum. It was also observed that red cell tethers steadily increase in length when the fluid shear stress is greater than approximately 1.5 dyn/cm(2) and tether lengths in excess of 200 mum have been achieved. Tethers appear to possess both fluid and elastic properties.