The anatomic description of the arterial supply of the muscles of the eyeball was studied because medial and lateral approaches to the orbit to treat various disorders might severely damage the main trunk of the ophthalmic artery. The different arterial pedicles for each muscle, as well as their origins and points of penetration into the muscle, were studied in 19 male human orbits. In all cases, the muscular branches originated from the ophthalmic artery, and generally from the inferior face of this artery, just after crossing the optic nerve. The inferomedial muscular trunk arose from the distal of the ophthalmic artery (63.16%). The inferolateral muscular trunk, the superior oblique, levator palpebrae superioris, superior rectus, lateral rectus, and medial rectus arose from the lacrimal artery (43.36%), the bend of the ophthalmic artery (36.84%), the supraorbital artery (36.84%), the distal end of the ophthalmic artery (52.6%), the lacrimal artery (89.47%), and the inferomedial muscular trunk (84.51%), respectively. Complications resulting from damaging the artery can cause inadequacy in eye position, mobility, superior oblique function, or binocular vision, which are expected to be corrected postoperatively.