We investigate the stress intensity factors for several crack configurations in G-11 woven glass/epoxy laminates with temperature-dependent properties under tension at cryogenic temperatures. A state of generalized plane strain is assumed. Cracks are assumed to have occurred in the transverse fiber bundles. Cases of a single stack and doubly-periodic arrays of cracks are considered. The order of stress singularities at the tip of a crack is obtained for the case where the crack is normal to and ends at an interface between two fiber bundles. A finite element method is used to determine the stress intensity factors at the crack tip of two-layered woven laminates. Special singular elements containing the exact stress singularity are placed around the crack tip. Numerical results for the stress intensity factor and the order of stress singularities at cryogenic temperatures are obtained and are presented in a graphical form.