The decarbonization of commercial aviation requires the adoption of climate-neutral propulsion systems, with liquid hydrogen (LH2) emerging as a leading candidate fuel. However, storing LH2 at cryogenic temperatures imposes severe thermo-mechanical loads on the containment structures, particularly during ground operations such as filling. When a cryogenic liquid enters a tank that is initially at ambient temperature, steep and non-uniform temperature gradients develop in the wall, which can induce substantial transient thermal stresses. Understanding these stresses is important for the safe design and operation of future aviation LH2 tanks. This study presents a finite element model to predict the transient stress evolution in cryogenic tanks during filling. The model represents a horizontal 2m long, 0.66m diameter, 316L stainless-steel cylinder with torispherical heads, based on the demonstrator under development in the Horizon Europe project ALRIGH2T. An elastic–plastic, temperature-dependent material model was developed from in-house cryogenic tests supplemented with literature data. The coupled transient thermal–mechanical numerical models were implemented in LS-DYNA. Experiments with liquid nitrogen, measuring distributed wall temperatures and induced strains throughout the filling process are foreseen as an initial validation step. The simulations show that pronounced local temperature gradients form near the moving liquid level, where each point on the wall undergoes a tension–compression stress cycle as the interface passes, with the maximum stresses occurring at the liquid height. Given the limited availability of literature data on stress fields in the inner tank of double-walled vacuum-insulated vessels, the results provide new insight into their thermo-mechanical behaviour under realistic operational transients.