The relationship between red blood cell mechanics and functional capillary density is examined. Experimental observations of capillary recruitment in skeletal muscle have shown sequential recruitment and derecruitment of capillaries fed by a single arteriole, implying that flow may cease in individual capillaries at small nonzero driving pressures. Such behavior is not expected in uniform blood-perfused tubes, but could occur when moving red cells encounter geometrical irregularities in capillaries. From known elastic properties of the red cell membrane, a lower bound is computed for the pressure required to sustain red cell motion in irregular capillaries. This may be an underestimate of the pressure required, because it neglects the viscous resistance of the red cell membrane when it undergoes transient deformations. Simulations including membrane viscosity show that viscous effects can substantially increase flow resistance. It is concluded that the mechanical properties of red blood cells can play a significant role in the modulation of functional capillary density.