A mathematical model is described which can be used to calculate blood flow in a normal artery from pressures measured at two separated points. The equations of motion of fluid in an elastic tube are simplified but sufficient realism is retained for the application to arterial flow. A numerical solution to the equations averaged over each section of the tube is chosen and these equations are solved by the method of finite differences. A substitution is made for the frictional term which cannot be expressed exactly in these nonlinear partial differential equations. The sensitivity of the results to changes in the friction term is demonstrated. A method is presented which bases the skin friction on a linear approximation, but within this limitation uses a value which is correct in magnitude and phase. A correction is made for entrace-length effects. The wall properties are represented by a pressure-radius relationship developed from previous work by the authors (Taylor and Gerrard, 1976). The use of the model is illustrated by using experimental data quoted by Streeteret al. (1963). The solution compares favourably with the experimental results.