The god Mercury opens Plautus's Amphitryon with a prologue of the play's background events. Amphitryon and his slave Sosia are returning to their native city of Thebes following a long period fighting a war abroad. While he was away, the god Jupiter, struck by the beauty of Amphitryon's wife, Alcmena, decided he must have her. Summoning his divine powers, the god disguised himself as her absent husband and enjoyed her with impunity.

Aware that Amphitryon will soon return, Jupiter orders his son Mercury to delay his arrival so that the god might further prolong his idyll. Mirroring his father's action, Mercury takes on the appearance of Sosia. When the real Sosia encounters his own image in Mercury, the two fight, and the god beats him badly. The baffled slave makes haste to his master's ship to report this bizarre turn of events to a skeptical and angry Amphitryon.

Still in a sour mood, Amphitryon arrives with Sosia at his home the next morning, just after the departure of Jupiter. Alcmena is confused that her husband, who had seemingly just left, has returned so quickly. Although at first equally confused, Amphitryon soon realizes that his wife has been unfaithful and becomes much angrier. Alcmena's confusion only worsens, since she believes she has was never unfaithful to her husband. The couple engage in a fierce war of words until Alcmena, believing herself the wronged party, is on the verge of leaving her husband. Amphitryon heads for his ship to get support for his position from his fellow soldier Naucrates, who is also his wife's kinsman.

Aware of all, Jupiter realizes he needs to solve the problem he created. Again taking on the guise of Amphitryon, he tries to deflect Alcmena's anger, apologizing to her for his recent behavior and begging her not to leave him. At length, she agrees.

Meanwhile, failing to locate Naucrates, Amphitryon returns home, and after wrangling with Mercury, and fighting with a Jupiter still disguised as himself, he is struck by the god with lightning. He awakens to find that his wife has given birth to two children; one, fathered by Jupiter, is Hercules, and the other is the son of Amphitryon. He is deeply honored by this shared paternity and, realizing that he and his family are now under the protection of Jupiter, rejoices in the event.