During isochoric heating by fast neutron irradiation, a high pressure is almost instantaneously built up inside the falling liquid jets in a HYLIFE inertial confinement fusion (ICF) reactor. It has been suggested that the jets will breakup as a consequence of negative pressure occurring during the relaxation1,2. This is important to both the subsequent condensation process and the chamber wall design. In this paper the mechanism of the relaxation of liquid jets after isochoric heating has been studied with both incompressible and compressible models. The transient pressure field predicted is qualitatively similar for both models and reveals a strongly peaked tension in the wake of a rarefaction wave. The pressure then rises monotonically in radius to zero pressure on the boundary. The incompressible approximation greatly over predicts the peak tension, which increases with time as the rarefaction wave moves toward the center of the jet. Since the tension distribution is as a narrow spike rather than uniform, a cylindrical fracture is the most likely mode of failure. This paper also discusses the available methods for estimating liquid tensile strength.