This paper presents an experimental and analytical investigation of the effect of specimen geometry on the tensile properties and damage behavior of glass fiber reinforced polymer woven laminates at cryogenic temperatures. Cryogenic tensile tests were performed on three types of specimens, and acoustic emission monitoring was employed to characterize the damage development during loading. A two-dimensional finite element analysis was also carried out for three tensile test specimens in order to have a thorough understanding of the progressive failure behavior. A comparison was made between simulation and experiment.