The epigastric artery (French : Artère épigastrique ; Latin :epigastrica inferior) arises from the fore part of the external iliac artery, usually a few lines above Poupart's ligament.

At first the artery inclines downwards, so as to get on a level with the ligament, and then changing its direction, passes obliquely upwards and inwards between the fascia transversalis and the peritoneum, to reach the rectus muscle of the abdomen. It then ascends almost vertically behind that muscle (being placed between it and its sheath, where this latter exists). Having given off lateral muscular branches, the epigastric artery terminates above the umbilicus in several offsets, which ramify in the substance of the muscle, and anastomose with the terminal branches of the internal mammary and inferior intercostal arteries; some of its branches communicate also with offsets from the lumbar arteries.

The epigastric artery is accompanied by two veins, which unite into a single trunk before ending in the external iliac vein.
In its course upwards from Poupart's ligament to the rectus muscle, the artery crosses close to the inner side of the internal abdominal ring ; and in this situation the vas deferens, escaping from the ring, turns behind the artery, in descending into the pelvis.
The branches of the epigastric artery are small, but numerous.
The cremasteric artery, a slender branch, accompanies the spermatic cord, and, after supplying the cremaster muscle and other coverings of the cord, anastomoses with the spermatic artery.
Several muscular branches arise from each side of the epigastric artery, ramify in the rectus muscle, and communicate with the branches of the lumbar and circumflex iliac arteries ; whilst others (superficial branches) perforate the abdominal muscles, and, when beneath the skin, join with branches of the superficial epigastric artery.
The epigastric artery also furnishes a small pubic branch, which ramifies behind the pubes, and communicates by means of a descending branch or branches with a similar offset from the obturator artery, as already described in treating of the branches of that vessel.

Peculiarities of the epigastric artery

This artery occasionally arises an inch and a half, or even two inches and a half, above Poupart's ligament, and it has been been to arise below that ligament from the femoral, or from the deep femoral. The epigastric frequently furnishes the obturator artery ; and on the other hand two examples are recorded in which the epigastric artery arose from the obturator, that vessel being furnished by the internal iliac artery.* In a single instance, the epigastric artery was represented by two branches, one arising from the external iliac, and the other from the internal iliac artery.** Some combinations of the epigastric with the internal circumflex, or with the circumflex iliac, or with both of these vessels, have been noticed.

From Quain's anatomy.