The present study develops the unsteady, nonlinear, two-dimensional partial differential equations for pulsatile flow in a flexible tube. The fluid is assumed to be a Newtonian, incompressible liquid similar to blood. The vessel is modeled as circular in cross section and tapering with increasing distance from the heart. The governing equations are solved numerically using a finite difference form of the Navier-Stokes equations and the Alternating Direction Implicit method. The purpose of this study is to solve a simplified version of the general equations in order to demonstrate the feasibility of solving this type of system numerically