The purpose of this investigation is to test the hypothesis that capillary pressure gradients are elevated in spontaneously hypertensive rats (SHR) and to determine the mechanism for the elevation. The cremaster muscle was prepared for microscopic examination under chloralose-urethane anesthesia in seven SHR and eight Wistar-Kyoto (WKY) rats 4-6 weeks of age. Capillary hematocrit, diameter, and red cell velocity were measured. Capillary flow induced by a time-varying pressure gradient was treated mathematically. A finite Hankel transformation was applied to the Navier-Stokes equation for capillary vessels. The solution was expressed as a Fourier-Bessel series, and the fluctuation of capillary flow induced by a time-varying pressure gradient was studied. It was shown that if the velocity fluctuation depended only on the pressure gradient, then the velocity fluctuation would be diminished almost instantly after the capillary started to flow. Capillary pressure gradient and shear stress were evaluated according to two different flow models, Newtonian and Casson. The capillary viscosity was obtained from the capillary hematocrit based on the empirical correlation of viscosity vs hematocrit. Calculations based on both flow models indicate that the capillary pressure gradient and shear stress of SHR is higher than in WKY, especially in vessels near 6 microns in diameter. The elevated pressure gradient is due to a combination of reduced capillary density, causing a higher red cell velocity and a tendency toward smaller capillary diameters in the SHR. Capillary hematocrit and viscosity were not elevated in the SHR.