In this article fully developed pulsed flow of an incompressible Newtonian fluid ( crude oil) through a pipe line has been modeled and analyzed using the finite element method and compared with results based on an analytical solution. The flow is generated by a periodic pressure gradient superimposed on a constant Poiseuille flow. The results show good agreement between analytical and numerical solutions based on finite element method for the Newtonian fluid under unsteady regimes. Results also indicate a smooth development of the transient centerline velocity evolution and of the spatial variation of the flow field, which is a consequence of the introduction of some physical diffusion in the equation of motion by means of the finite solvent viscosity. There are minor discrepancies in the simulation of fast oscillation during those parts of the solution cycle where the flow near the boundary moves in the opposite direction to that in the core of the pipe. Also, results show that the phase difference between the core and the boundary layer gives rise to an annular flow pattern during fast oscillations.