A basic mathematical model of human red cells is presented which integrates the charge and nonideal osmotic behavior of hemoglobin and of other impermeant cell solutes with the ion transport properties of the red cell membrane. The computing strategy was designed to predict the behavior of all measurable variables in time in ways that optimize comparison with experimentally determined behavior. The need and applications of such a model are illustrated in three separate examples covering different areas of experimentation in the physiology and pathophysiology of red cells.