The elongation curve of RBC as determined by rheoscopy or ektacytometry (laser diffraction) resembles a rectangular hyperbola. The experimental data obtained so far included too large errors of measurement to allow precise mathematical description. The combination of laser diffraction with image analysis has improved ektacytometry considerably, such that the error of measurement is reduced to less than 0.5%. In laminar flow RBC of healthy donors are elongated elliptically (p <EQ 0.001). Using the precise data of elliptical deformation, the elongation curve can be described to be hyperbolic. Hence, the double reciprocal plot gives a linear curve which -- over a wide range of shear stress (15 to 500 dyn/cm2) -- fits well the experimental data (r >= 0.99: p <EQ 0.001). The stress strain characteristics (i.e. elongation curve) can be described by two parameters: maximum elongation (Emax) and the shear stress needed for half-maximum elongation (KE).© (1994) COPYRIGHT SPIE--The International Society for Optical Engineering. Downloading of the abstract is permitted for personal use only.