An extraocular muscle support sling and a method for surgically implanting the sling to reinforce a weak or ineffective extraocular muscle. The sling includes a semi-flexible anchor base and a pair of elastic arms which extend from the anchor base and are held together to create a loop. During implantation, the anchor base of the sling is attached to a movable target tissue of the patient, and the looped elastic arms are attached to an immobile base tissue. A pulling or tensioned force applied to the elastic arms causes the patients movable target tissue to which the anchor base is attached to be pulled towards and oriented with respect to the immobile base tissue with the same force and in the same direction as would be the case had the muscle been normal. According to preferred embodiments, the extraocular muscle support sling has particular application for treating ptosis and strabismus.