We do not often think of Old Testament players as "Saint". We do not say St. David or St. Moses, but we believe that they are, because we believe that Christ opened the gates of Heaven and all the souls that had been waiting were granted admittance. Elijah is celebrated in both the East and the West.
Elijah's name takes the two names for God used in the Pentateuch and brings them together: "my God is Y**H" or simply, "El[ohim] is Y**H". There is only one God, though we recognize His distinct aspects, what we would call "persons", and that is what Elijah's name points out.
Aside from that powerful theological witness, Elijah is also the patron of desert monks, especially the Carmelites, because he defeated the prophets of Baal on Mt Carmel and took refuge in a cave on Mt. Horeb and found God there.
He left his servant there and went a day’s journey into the wilderness, until he came to a solitary broom tree and sat beneath it. He prayed for death: “Enough, LORD! Take my life, for I am no better than my ancestors.” He lay down and fell asleep under the solitary broom tree, but suddenly a messenger touched him and said, “Get up and eat!” He looked and there at his head was a hearth cake and a jug of water. After he ate and drank, he lay down again, but the angel of the LORD came back a second time, touched him, and said, “Get up and eat or the journey will be too much for you!” He got up, ate, and drank; then strengthened by that food, he walked forty days and forty nights to the mountain of God, Horeb. There he came to a cave, where he took shelter. But the word of the LORD came to him: Why are you here, Elijah? He answered: “I have been most zealous for the LORD, the God of hosts, but the Israelites have forsaken your covenant. They have destroyed your altars and murdered your prophets by the sword. I alone remain, and they seek to take my life.” Then the LORD said: Go out and stand on the mountain before the LORD;* the LORD will pass by. There was a strong and violent wind rending the mountains and crushing rocks before the LORD—but the LORD was not in the wind; after the wind, an earthquake—but the LORD was not in the earthquake; after the earthquake, fire—but the LORD was not in the fire; after the fire, a light silent sound. When he heard this, Elijah hid his face in his cloak and went out and stood at the entrance of the cave. A voice said to him, Why are you here, Elijah?
-- 1 Kings 19:3b-13
Things to Think About