Single human red cells were suspended in media with viscosities ranging from 12.9 to 109 mPa s and subjected to shear flow ranging from 1/s to 290/s in a rheoscope. This is a transparent cone-plate chamber adapted to a microscope. The motion of the membrane around red cells oriented in a steady-state fashion in the shear field (tank-tread motion) was videotaped. The projected length and width of the cells as well as the frequency of tank-tread motion were measured. One-thousand eight-hundred seventy-three cells of three blood donors were evaluated. The frequency increased with the mean shear rate in an almost linear fashion. The slope of this dependence increased weakly with the viscosity of the suspending medium. No correlation was found between the frequency and four morphological red cell parameters: the projected length and width of the cells as well as the ratio and the square root of the product of these quantities. The energy dissipation within the red cell membrane was estimated based on the measured parameters and compared to the energy dissipation in the undisturbed shear flow. At constant mean shear rate the rise of the energy dissipation with viscosity is slower whereas at constant viscosity the rise with the shear rate is steeper than in the undisturbed shear flow. A fit of the data collected in this work to a theoretical red cell model might allow one to determine intrinsic mechanical constants in the low deformation regime.