Odysseus, as a noble Greek warrior, is expected to possess great physical strength, and, in a number of places throughout The Odyssey, Odysseus displays feats of strength far in excess of anything anyone else could do. When he returns at long last to Ithaca, disguised as a beggar, he accepts Penelope's challenge to shoot an arrow through the gaps of twelve axes lined in a row. But this is not the real test of strength; it's the fact that Odysseus is able to string the bow in the first place that shows this. No other man could possibly hope to perform this great feat, and all the suitors fail.

Stabbing out the eye of the Cyclops Polyphemus was another example of Odysseus's enormous strength. He uses a large stake which he needs to lift up all by himself before driving it deep into Polyphemus's eye. And that takes some doing. Also, Odysseus, at the prompting of Tiresias the blind seer, lifts a huge wooden oar and carries it over his shoulder, walking so far inland that people won't know what it is. They'll think it's a winnowing fan. Odysseus can then make a sacrifice to Poseidon, god of the sea and cause of most of Odysseus's trials and tribulations.

Much of what Odysseus does in The Odyssey shows how clever and crafty he is. However, he is one of the most heroic soldiers of the Trojan War. Had he not been physically strong, he could not have held such respect among his men.

The best example of Odysseus's physical strength comes with the test of the suitors by Penelope. Odysseus is the only man strong enough to string the bow (although his son, Telemachus, comes closest). After his identity is revealed, Odysseus slays every man in the room. He is indisputably the strongest of all the men who want Penelope, not simply the smartest.