A continuum mechanics model of sickled red blood cells in a narrow capillary is developed based on the viscometric studies of polymerized sickled hemoglobin solutions by Chien et al. (1982). That study as well as other published experimental data have suggested the rheology of a sickled red blood can be represented by a Voigt solid bounded by an elastic membrane. Here the relative contributions of the red cell membrane and intracellular hemoglobin solution (with or without polymer) to the overall sickle cell deformability is studied. The model describes how the amount of polymer inside a sickle erythrocyte changes its elasticity and viscosity and therefore influences the deformability and flow resistance of the cell at different oxygen (O2) saturation levels.