A set of governing equations comprising linear momentum, mass, and heat transfer is presented for thermoelastic freezing of a porous material. The theory of unsaturated freezing porous media is introduced to model deformation of concrete, a traditional building material, whose pore network is pressurized by the wet air, frozen ice, and unfrozen water. A general solution scheme is provided for the appropriate boundary conditions pertaining to the primary concrete containment in a liquefied natural gas tank, and simulated results are analyzed for fully and partially saturated non-air-entrained concrete and fully saturated air-entrained concrete. Effect of cooling rate is also demonstrated. It is found that high cooling rate results in high expansion provoked by high hydraulic pore pressure and the corresponding suppression of pore liquid freezing temperature. It is also revealed that air-entrained concrete, by allowing quick dissipation of the displaced pore water and accommodating the ensuing ice formation, shows less contraction and subsequently less crack initiating stresses than the high-porosity, non-air-entrained concrete. Similar outcomes are observed near the concrete surfaces subjected to evaporation prior to cryogenic freezing. High hydraulic pressure, induced by the delayed dissipation of excess pore water, is likely to generate at the center of surface-dried concrete walls.