Velocity-dependent flow of human red blood cells in capillaries with inside diameters of 4 to 8 micron is described theoretically. Cells are assumed to flow in single file, with axisymmetric shapes. Plasma flow in the gaps between cells and vessel walls is described by lubrication theory. The model takes into account the elastic properties of red cell membrane, including its responses to shear and bending. Cell shape is computed numerically as a function of tube diameter and cell velocity over the range 0.001 to 10 cm/sec. Relative apparent viscosity and dynamic hematocrit reduction (Fahraeus effect) are also computed. Since effects of interactions between cells are neglected, the Fahraeus effect is independent of hematocrit, while viscosity varies linearly with hematocrit. At moderate or high cell velocities, about 0.1 cm/sec or more, cell shapes and rheological parameters approach flow-independent limits. At lower velocities, cells broaden as a result of membrane shear and bending resistance and approach the walls more closely. Consequently, apparent viscosity increases with decreasing flow rate. Predicted values are in agreement with in vitro experimental determinations. Flow cessation is not predicted to occur in uniform tubes at positive driving pressures. Elastic deformational energies associated with red cell shapes are computed, leading to estimates of the pressure difference required to drive red cells past typical irregularities in capillary lumen cross sections. The hindrance to flow resulting from such structural irregularities represents a potential rheological mechanism for cessation of capillary flow at very low driving pressures.