Desire Under the Elms was inspired by plot elements and characters from the Euripides play Hippolytus. In it, Phaedra, Theseus' wife, attempts to seduce his son, chaste Hippolytus. After this fails and Hippolytus threatens to reveal her unfaithfulness, Phaedra commits suicide. Theseus finds a letter that Phaedra carried accusing Hippolytus of raping her. Enraged, Theseus (using one of three wishes that his father Poseidon promised him) curses his son with banishment or death. After Hippolytus is fatally wounded by an encounter with a bull, Artemis arrives to reveal the truth to Theseus, and Hippolytus dies after absolving his father.
The characters Eben, Abbie, and Ephraim roughly correspond with Hippolytus, Phaedra, and Theseus respectively. Both plays are driven by a love triangle between a father, a son, and a stepmother, and the tragedy arises from misguided actions made by the stepmother. In Phaedra's case it is her lust of her husband's son and the falseness of her letter. O'Neill takes this one step further in '’Desire Under the Elms'’ and makes Abbie's misguided actions the begetting and murder of her child.
In Desire Under the Elms: In the Light of Strindberg’s Influence, Murray Hartman also saw strong parallels between Desire Under the Elms and the work of August Strindberg, writing "At any rate, there is hardly a plot element in the play that cannot be traced to one or more sources in Strindberg." He details several elements of O'Neill and Strindberg's biographies that are similar, and how they manifest in Desire Under the Elms, in addition to naming several specific works of Strindberg's, such as The People of Hemsö, The Bridal Crown, and The Son of the Servant. Specifically, he points out very similarly confused relationships with the writers' respective mothers and contentious relationships with their fathers. He also writes, "The basic situation, where the young son has seen his beloved mother worked to death by a hard father and then has had to bear the usurpation of her position by an aggressive stepmother, has its origin in The Son of a Servant." This can be seen in Desire under the Elms through Eben's opinion that Ephraim worked his mother to death and largely drives the plot.