The Sudarium of Oviedo has been studied intensively with a petrographic (polarizing) microscope. It is composed of pure flax fibers, and they show the same characteristics as the Shroud of Turin. The technology used to prepare the linen cloth appears to be identical to that described for Roman times by Pliny the Elder (Natural History XIX, 3, 16-18). Flax fibers are mostly crystalline cellulose, and the crystals have a fibrillar structure. The fibers are birefringent between crossed polarizers; however, the birefringence changes depending on the past history of the material. Perfect, new flax fibers show extinction (the segments between growth nodes are perfectly black) at two angles as the microscope stage is rotated. Strained or irradiated fibers show zones of birefringence at other angles. Fibers from the Sudarium show many defects caused by different kinds of radiation. The evidence indicates significant age for the material. It seems to have similar defect types and populations as the Shroud of Turin. The two cloths must be roughly the same age.