The pressure relief system of liquid helium cryostats requires a careful design, due to helium's low enthalpy of vaporization and due to the low operating temperature. Hazard analyses often involve the failure of the insulating vacuum in the worst-case scenario. The venting of the insulating vacuum and the implications for the pressure increase in the helium vessel, however, have not yet been fully analyzed. Therefore, the dimensioning of safety devices often requires experience and reference to very few experimental data. In order to provide a better foundation for the design of cryogenic pressure relief systems, this paper presents an analytic approach for the strongly dynamic process induced by the loss of insulating vacuum. The model is based on theoretical considerations and on differential equation modeling. It contains only few simplifying assumptions, which will be further investigated in future experiments. The numerical solutions of example calculations are presented with regard to the heat flux into the helium vessel, the helium pressure increase and the helium flow rate through the pressure relief device. Implications concerning two-phase flow and the influence of kinetic energy are discussed.