Liquefied natural gas (LNG) is stored at a cryogenic temperatures ≤ -160°C and around atmospheric pressure to insure the minimum storage volume in tanks. The demand for LNG has been increasing as a primary source of energy. Therefore, there is significant interest in the construction of LNG tanks to achieve low cost and safe storage. Three systems are typically used to store LNG: single containment, double containment, and full containment. Concrete is used in these containment systems, and consequently, understanding concrete behavior and properties at cryogenic temperatures is important. The research documented in this thesis deals with computational analysis of the behavior of concrete subjected to cryogenic temperatures. The analysis focuses on the effect of aggregate sizes, coefficient of thermal expansion, volume fraction, and the shape of aggregate on damage of concrete subjected to cryogenic temperatures. The analysis is performed by developing a computational model using the finite element software ABAQUS. In this model, concrete is considered as a 3- phase composite material in a meso-scale structure: mortar matrix, aggregate, and interfacial transmission zone (ITZ). The Concrete Damage Plasticity model in ABAQUS is used to represent the mortar and ITZ phases of concrete. This model has the advantage of accounting for the effect of temperature on material properties. The aggregate phase is modeled as a linear-elastic material. The model parameters are selected based on comprehensive literature review of material properties at different temperatures. The finite element results provide very useful insight on the effects of concrete mixture design and properties on resistance to damage. The most important factor that affected damage development was the difference in the coefficient of thermal expansion between the mortar and aggregates. Models in which the mortar and aggregate had close values of positive coefficients experienced less damage. The model with irregular shape particles experienced more localized damage than the model with circular shape particles. The model was successful in demonstrating the effect of using air entrained concrete in reducing damage. The damage results predicted by the model for air entrained and non-air entrained concrete are validated by comparing them with experimental data from the literature. The analysis validated the capabilities of the mode in simulating the effect of reduction in temperature on damage. The modeling results and the findings from the literature review were used to put forward recommendations regarding the characteristics of concrete used in LNG storage.