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The behaviour of a small disturbance in an arterial blood flow has been studied analytically. The growth equation governing growth or decay of a disturbance has been obtained and solved. The behaviour of wave amplitude has been investigated as the wave propagates in time. The application of results to the human arterial system shows that the shock waves are not expected under normal physiological conditions. In the case of a pathologically increased pressure rise at the root of aorta, shock-like transitions may develop in the periphery. It is observed that the friction effects are to resist the tendency of shock formation in arteries.