Desire Under the Elms tells the story of five characters on a rural farm in 1850s' New England and how their lives are both pushed together and pulled apart by their conflicting desires.

The play opens by introducing Cabot's three sons, Eben, Simeon, and Peter. In their first conversation, they voice their mutual resentment towards their father and their various desires: Eben wants to own the farm (which he believes belonged to his dead mother and is now rightfully his), while his older brothers Simeon and Peter yearn to leave and seek their fortunes in California. Eben is restless and seeks sexual comfort from a girl in town; he treats her as a sexual outlet and is seemingly comfortable with his lustful desires, even as he seems to be trying to prove his masculinity rather than to find a real connection. The inciting incident of the plot comes toward the end of Part One. Cabot brings home a new bride, Abbie, and her arrival sets into motion a shift in family dynamic with profound consequences. Generally, Eben is the protagonist, Cabot the antagonist, and Abbie a foil, but all three characters are sympathetic in various ways and take on different roles in pushing the action forward. After Simeon and Peter leave the farm at the end of Part One, tension begins to emerge between the three characters left to tend the farm.  

Part Two begins with Abbie and Eben verbally sparring with each other about who owns the farm and house, important and meaningful assets. Abbie adds to the conflict between Cabot and his son because she covets the house—as an orphan, having her own home is a dream of hers. All three characters want to own the farm and house themselves, but a deeper desire at play is to make a meaningful human connection. Cabot seems to show tenderness towards Abbie and he makes it clear that he loves her, but he also continually says that no one can understand him, including her. Eben rejects Abbie's flirting and tries to deny his attraction to her, afraid to dishonor the memory of his mother, but he is drawn to Abbie in spite of himself. Abbie seems to be luring Eben in as if playing a game, but we learn that she also desires love and connection. A pivotal moment of the play comes when Eben and Abbie finally declare their love for each other, succumbing to their mutual attraction and desire for a loving connection. In discussing Eben's mother's presence in the house, they eventually agree that being together will not dishonor her memory. Eben finds comfort and release in being with Abbie and happiness in the idea that his mother can rest in peace.  

The final part of the play leads to a tragic conclusion. Abbie has borne a baby that Cabot believes to be his, but the audience, as well as the neighbors, knows it belongs to Eben. The celebration party demonstrates the important, though rare, communal aspect of life in that time and place, including the music and dancing that attends social gatherings. But it also illustrates the isolation of the main characters from their neighbors. Although Cabot joins the celebration, the neighbors gossip behind his back and it's clear Cabot does not get along with them. Eben stays upstairs in the bedroom, and Abbie sits off to the side, eventually joining Eben. They have no interest in socializing. Abbie is only interested in being with Eben and Eben is conflicted about having to keep quiet about the baby being his.  

The argument in Scene Two between Cabot and Eben leads to serious consequences. Cabot succeeds in pitting Eben against Abbie once more, using Eben's insecurity about whether Abbie really loves him or only wants to own the farm. After Abbie breaks up their physical altercation, Cabot leaves her and Eben, triumphant from physically and emotionally besting his son. In the conversation between Abbie and Eben, there is a return to their arguments from before, but Abbie does not tease or fight back at this point. Eben accuses her of using him to get the farm and bear a son and declares he's leaving, wounded from feeling used. Abbie is desperate to prove her love to him and hints at what she might do since it seems clear to her that the baby is what has come between them.  

In Scenes Three and Four, the action consists of the aftermath of the infanticide that Abbie commits. Eben's reaction to this illustrates his growing love and possessiveness towards the baby. The tragedy at this point is twofold for Abbie—she has killed her baby but also angered and alienated Eben even more with her desperate attempt to win back his love. While Eben is gone to get the sheriff, Abbie tells Cabot what she's done and goes from an unemotional shock to a wild emotional state, confessing everything to him about her and Eben. Cabot is affected by this in various ways. He is dazed, shocked, hardened, and then emotional again as he tells her he loves her and claims wouldn't have turned her in as Eben is doing, even as his previous interactions with his family might suggest otherwise. In the final moments of the play, Eben returns and makes amends with Abbie, insisting on sharing her punishment. Their reconciliation creates a bittersweet ending: they have avowed their mutual love but must face possible fatal punishment for the death of their child. The other tragedy at the end of the play falls on Cabot. He is left alone on the farm, with no male heirs or companions, a fate he has arrogantly tried to prevent but has brought on himself.  

The play is a study of the complexity of individuals' desires and how they play out in various relationships. It also uses the themes of nature and religion as backdrops to these dramas: the presence of God is a powerful concept that motivates and informs characters' feelings and actions, particularly Cabot. Nature is a presence all around the characters: the farm is part of the natural world from which they make their living, and the beauty of the sky is something they all admire. It is a power larger than them, an omniscient and objective presence, making their lives seem small but also reflecting their foibles, like the elm trees that surround the house, framing the drama as one that plays out again and again, as cyclical as the seasons.