Examination of right and left sides in cadavera of 76 adults and 24 children give the following results: (1) The internal maxillary artery lay lateral to the external pterygoid muscle more frequently in dolichocephalic than in brachicephalic heads. (2) When the artery was medial to the external pterygoid it was most commonly lateral to the inferior alveolar and lingual nerves, but sometimes was medial to both nerves, sometimes medial to the inferior alveolar and lateral to the lingual, and occasionally the artery perforated the inferior alveolar but crossed lateral to the lingual nerve. (3) In adults, the artery formed an arc convex upward or a considerable elevation, but in children it was more horizontal. The application of these findings to the surgical puncture of the trigeminal (Gasserian) ganglion and to ligation of the internal maxillary artery is indicated.