Our aim in this paper is to use a simple theoretical model of the intraspinal cerebrospinal-fluid system to investigate mechanisms proposed for the pathogenesis of syringomyelia. The model is based on an inviscid theory for the propagation of pressure waves in co-axial, fluid-filled, elastic tubes. According to this model, the leading edge of a pressure pulse tends to steepen and form an elastic jump, as it propagates up the intraspinal cerebrospinal-fluid system. We show that when an elastic jump is incident on a stenosis of the spinal subarachnoid space, it reflects to form a transient, localized region of high pressure within the spinal cord that for a cough-induced pulse is estimated to be 50 to 70 mm Hg or more above the normal level in the spinal subarachnoid space. We propose this as a new mechanism whereby pressure pulses created by coughing or sneezing can generate syrinxes. We also use the same analysis to investigate Williams' suck mechanism. Our results do not support his concept, nor, in cases where the stenosis is severe, the differential-pressure-propagation mechanism recently proposed by Greitz et al. Our analysis does provide some support for the piston mechanism recently proposed by Oldfield et al. and Heiss et al. For instance, it shows clearly how the spinal cord is compressed by the formation of elastic jumps over part of the cardiac cycle. What appears to be absent for this piston mechanism is any means whereby the elastic jumps can be focused (e.g., by reflecting from a stenosis) to form a transient, localized region of high pressure within the spinal cord. Thus it would seem to offer a mechanism for syrinx progression, but not for its formation.