For constructing marine liquefied natural gas (LNG) fuel/storage tanks, high manganese steel is being recognized as an alternative to stainless steel, nickel alloy, and aluminum alloy. In this study, the nonlinear tensile behavior of high manganese steel was investigated and numerically simulated at cryogenic temperatures at which natural gas exists as a liquid. Physical experimental tensile tests were carried out for a flat test specimen at 293 K and 110 K. In particular, the tensile behavior of a flat hole-notched high manganese steel specimen was experimentally obtained. A specimen with a hole was readily fractured compared to one without a hole. Tensile behavior of high manganese steel at the two cryogenic temperatures was compared to that of stainless steel, nickel, and aluminum alloy. In addition, numerical tests were performed for flat tensile specimens under identical experimental conditions. The elastoplastic damage model was derived and implemented using an Abaqus user-defined subroutine to appropriately simulate material behavior and degradation. The influence of some parameters on tensile behavior was investigated. The simulation results satisfactorily replicated the nonlinear tensile behavior of high manganese steel. The proposed numerical method, which is based on the damage-coupled material constitutive model, can be applied to structural analysis on the finite element analysis platform considering mechanical nonlinearities induced by severe conditions such as cryogenic temperature.