At the onset of the play, Ajax is enraged because Achilles' armor was awarded to Odysseus, rather than to him. He vows to kill the Greek leaders who disgraced him. Before he can enact his revenge, though, he is tricked by the goddess Athena into believing that the sheep and cattle that were taken by the Achaeans as spoil are the Greek leaders. He slaughters some of them, and takes the others back to his home to torture, including a ram which he believes to be his main rival, Odysseus.
Ajax realizes what he has done and is extremely upset that Athena fooled him and is sure that the other Greek warriors are laughing at him. Ajax contemplates ending his life due to his shame. His concubine, Tecmessa, pleads for him not to leave her and her child unprotected. Ajax then gives his son, Eurysakes, his shield. Ajax leaves the house saying that he is going out to purify himself and bury the sword given to him by Hector. Teukros, Ajax’s brother, arrives in the Greek camp to taunting from his fellow soldiers. Kalchas warns that Ajax should not be allowed to leave his tent until the end of the day or he will die. Tecmessa and soldiers try to track him down, but are too late. Ajax had indeed buried the sword, but has left the blade sticking out of the ground and has impaled himself upon it. Tecmessa is the first to discover Ajax impaled on his sword, with Teukros arriving shortly after. Menelaus appears on the scene and orders the body not to be moved. Ajax's half-brother Teukros intends on burying him despite the demands of Menelaus and Agamemnon that the corpse is not to be buried. Odysseus, although previously Ajax's enemy, steps in and persuades them to allow Ajax a proper funeral by pointing out that even one's enemies deserve respect in death, if they were noble. The play ends with Teukros making arrangements for the burial (which is to take place without Odysseus, out of respect for Ajax).