The existing computational model studies of pulsatile blood flow in arteries have assumed either rigid wall characteristics or elastic arterial wall behavior with wall movement limited to the radial direction. Recent in vivo studies have identified significant viscoelastic wall properties and longitudinal wall displacements over the cardiac cycle. Determining the nature of these movements is important for predicting the effects of ultrasound clutter in Doppler ultrasound measurements. It is also important for developing an improved understanding of the physiology of vessel wall motion. We present an analytically-based computational model based on the Womersley equations for pulsatile blood flow within elastic and viscoelastic arteries. By comparison with published in vivo data of the human common carotid artery as well as uncertainty and sensitivity analyses, it is found that the predicted waveforms are in reasonable quantitative agreement. Either a pressure, pressure gradient or volumetric flow rate waveform over a single cardiac cycle is used as an input. Outputs include the pressure, pressure gradient, radial and longitudinal fluid velocities and arterial wall displacements, volumetric flow rate and average longitudinal velocity. It is concluded that longitudinal wall displacements comparable to the radial displacements can be present and should be considered when studying the effects of tissue movement on Doppler ultrasound clutter.