The blue eye sockets of infants are considered to be caused by poor sleep, thin skin, iron deficiency anemia and indigestion. 1. Poor sleep: If infants do not have enough sleep or rest, they may have blue eye sockets. In addition, infants with thin eyelid skin may show signs of blue eye sockets because of the blood vessels under the skin. 2. Iron deficiency anemia: because of irrational diet structure, unbalanced nutrition, iron deficiency or intestinal parasitic infection, causing iron loss in the body of the child, which may lead to pallor and bluish around the eyes. 3. Indigestion: Due to low gastrointestinal function, babies can not get enough nutrition, which can cause children’s face to be thin and yellow, and the eye sockets to be blue and other discomforts. It is recommended that children with obvious blue eye sockets and other discomforts should consult a doctor promptly to assess their condition and follow the doctor’s instructions for treatment.