The density of different gaseous fuels can be increased for storage and transportation purposes trough the liquefaction process. The gases are converted to cryogenic fluids if liquefied by reducing their temperatures (e.g. for liquid hydrogen, LH2, and liquefied natural gas, LNG). Therefore, these cryogenic fuels must be stored in extremely well insulated tanks (double walled type with evacuated insulation). The ignition of an accidental fire in the vicinity of the cryogenic tank might cause the loss of integrity of the vessel. This event might lead to the catastrophic rupture of the vessel and provoke a major accident with many severe consequences. For this reason, the estimation of a potential time to failure (TTF) of the container in the worst-case scenario is critical. In this study, an analytical model was developed based on well-known thermodynamic equations, to estimate the heat transfer between the cryogenic tank and the surrounding fire in the worst-case scenario. The thermal conductivity of the double walled tank insultation is one of the most complex and critical parameters to evaluate. Different uncertainties regarding the vessel insulation were highlighted in the manuscripts. The outcomes of this model were validated against experimental results. Additional experimental tests are necessary to thoroughly validate the model and understand the behavior of the cryogenic vessels when exposed to a fire. This type of tests will be conducted for LH2 during the Norwegian project SH2IFT.