Orestes, son of Agamemnon, meets an old and faithful friend, Pylades, at the court of Pyrrhus, king of Epirus. In answer to the latter's inquiry, Orestes informs him of the reason for his presence. The Greeks are worried about the news that Pyrrhus has fallen in love with his prisoner Andromache, Hector's wife, and for her sake is protecting her son Astyanax. They have dispatched a mission to claim Astyanax, for he constitutes a potential danger to them. Orestes, in love with Hermione, Pyrrhus' neglected fiancée, has volunteered to head the mission, for he finds in it an excellent pretext to see Hermione again and perhaps take her back with him. First, however, he presents his demands to Pyrrhus, who haughtily rejects them. But his refusal is conditional on the love of Andromache.
Aware of Pyrrhus' hesitance, Hermione plans to return to her father, King Menelaus. She informs Orestes of her decision to follow him if Pyrrhus persists in defying the Greeks. Orestes briefly rejoices until Pyrrhus, stung by Andromache's coldness, decides to give in to his demands.
Orestes, enraged by the turn of events, plots to kidnap Hermione, who is unaware of his plan. Andromache, meanwhile, pleads unsuccessfully with Hermione to save her son. Then she turns to Pyrrhus, who demands her hand in marriage in return for his protection. Andromache, unable to come to a decision, goes to consult the spirit of her husband at his tomb.
Andromache has decided to yield to Pyrrhus, but with a tragic private reservation. She plans to kill herself directly after the wedding ceremony. Hermione retaliates for her rejection by Pyrrhus by imperiously demanding that Orestes kill Pyrrhus at the altar. She is hardened in her resolution by a last conversation with Pyrrhus, which confirms his indifference.
After Pyrrhus' departure, Hermione is violently torn between love and resentment. Resentment wins out when Cleone, her confidante, informs her of Pyrrhus' insulting happiness during the marriage ceremony. Yet, far from rejoicing when she hears Orestes' account of how the Greeks have avenged her by killing Pyrrhus at the altar, she curses him and stabs herself on Pyrrhus' body. Orestes is overwhelmed by despair and then madness.