It is a generally accepted hypothesis of renal physiology that the kidney forms urine from the blood by means of a complicated flow system consisting of renal tubules and capillaries. To obtain an understanding of the process of urine formation, a mathematic model of the kidney is made in terms of a boundary value problem for a system of differential equations. The object of this research is to provide a mathematical analysis of these boundary value problems. The analysis will utilize contemporary mathematical techniques that have been developed to study nonlinear boundary value problems. The analysis will provide a solid foundation for the kidney modeling effort and will aid in the development of more accurate and efficient procedures for the numerical solution of renal flow problems.