Hannah Kent’s Burial Rites tells a fictional account of the story of Agnes Magnúsdottir, the last person executed in Iceland (in 1830). As the story begins, Agnes has already been convicted of the murders of Natan Ketilsson and Pétur Jónsson and condemned to death for the crime, along with her coconspirators Fridrik Sigurdsson and Sigga Gudmundsdóttir. District Officer Jón, Jón’s wife Margrét, and their daughters Lauga and Steina are all given notice that District Commissioner Blöndal has decided that Agnes will be housed at their farm, Kornsá. The family is not happy about this, but they have no choice. Meanwhile, Assistant Reverend Tóti is told that Agnes requested him as her spiritual advisor. Tóti accepts the position, and he and the women of the Kornsá family all greet Agnes and her guards as she arrives at the farm.
At first the family at Kornsá is hostile towards and skittish around Agnes. Agnes helps with their chores and, when she is not working, she talks with Tóti, who visits frequently. Agnes tells Tóti she chose him as her minister because she met him once crossing a river. Tóti eventually realizes that Agnes needs someone to listen to her, and so each time Tóti visits, Agnes tells him a little more about her past. Tóti also looks in the ministerial book of Agnes’s childhood parish for information, and it is there that he learns about who Agnes’s mother and father were. When he talks to Agnes about her family, Agnes tells him that her mother Ingveldur abandoned her as a child and also lied about her real father. Agnes has two siblings, but one is dead and she does not know where the other is. Agnes also tells Tóti about the traumatic death of her beloved foster mother, Inga, who died in childbirth.
One day Blöndal calls upon Tóti to describe his methods with Agnes, and Tóti explains that they mostly just talk. Blöndal, unsatisfied, tells Tóti the details of Agnes’s alleged crime. According to Blöndal, Agnes, who was living with Natan and Sigga, was the mastermind of the murders. Blöndal thinks Agnes killed Natan out of jealousy for his interest in Sigga. Fridrik hit both Natan and Pétur several times with a hammer, but Blöndal believes that Agnes was the one who finished Natan off by stabbing him with a knife. After the murders, Agnes and Fridrik burned down the farm in attempt to conceal their murders. Blöndal believes that Sigga, if she knew about the murder plot at all, was being manipulated by Agnes. After hearing Blöndal’s perception of the murders, Tóti struggles to reconcile the woman he knows with the crime that Blöndal alleges Agnes committed. Still, he continues to see and talk to Agnes.
Meanwhile, Agnes slowly wins over the family at Kornsá. Steina is the first to befriend Agnes, because Steina remembers that she met Agnes once as a child while traveling and Agnes was kind to her. It is through Steina that Agnes learns that Sigga has received an appeal on her sentence so she will not be executed. Margrét, who suffers from a debilitating cough, appreciates Agnes’s help around the house. Agnes gains Margrét and Jón’s respect when she helps their neighbor Róslín safely deliver her at-risk baby. Lauga, on the other hand, hates Agnes more and more the closer Agnes gets to the other members of the family.
Through Agnes’s conversations with Tóti, the reader learns that, after Agnes’s foster mother died, Agnes had no stable home. Agnes worked on various farms throughout her young adulthood, where she was often subjected to sexual violence. Agnes ran into her half-brother, Jóas, while traveling, and the two of them went to work together on Worm Beck’s farm. One night after Jóas and Agnes got into a fight, Jóas stole Agnes’s money and left. Agnes had another friend on the farm named María, and it was María who first pointed out Natan to Agnes. Natan and Agnes struck up a friendship during Natan’s visits to see Worm, and then they started a romance. María, who did not like Natan, stopped speaking to Agnes. Eventually, Natan asked Agnes to come live with him and be his housekeeper.
At some point, Agnes admits to Tóti that she asked him to be her spiritual guide not only because they met when they were crossing the river, but also because Agnes once had a dream that Tóti helped her across a field of snow—before she even met him. Meanwhile, the family at Kornsá goes through the fall traditions together, slaughtering animals and harvesting hay for winter.
Agnes tells Tóti, with the family at Kornsá often listening, how she made the trip to Natan’s farm, where she first met Sigga. Sigga also claimed to be Natan’s housekeeper. When Agnes asked Natan about the confusion, Natan told her Sigga was just stupid. Agnes and Natan’s romance continued at the farm, though Natan was away often. They hid the affair from Sigga. Natan’s ex-lover Rósa also visited the farm at some point to drop off their daughter, Thóranna, and she acted somewhat hostile towards Agnes. Natan’s neighbor Fridrik came to visit often as well, though he and Natan fought because Fridrik was constantly trying to steal Natan’s money. Fridrik and Sigga began to fall in love.
One day, Tóti falls gravely ill and cannot go to Kornsá for weeks. Agnes misses Tóti and wonders why he has stopped coming. She holds out some hope that somehow she will get an appeal like Sigga did. Her relationships with the other members of the Kornsá household continue to improve.
One night, Agnes and Margrét wake up in the middle of the night and begin talking. Agnes tells Margrét how her relationship with Natan began to deteriorate as Natan became moody and withdrawn. Natan told Agnes one day that he kept having dreams about his own death and Agnes was in them. Natan then became violent toward Agnes. One night, Agnes woke up and saw Natan having sex with Sigga, realizing that he had been sleeping with both of them the whole time. In the meantime, Fridrik asked to marry Sigga, and Natan agreed to let her. One night, Agnes confronted Natan about sleeping with Sigga, and Natan threw her out in the snow in a rage. Agnes then went to Fridrik’s house for shelter. Agnes and Fridrik went back to Natan’s farm the next day while Natan was gone, planning to leave and take Sigga with them. However, Sigga told Fridrik that Natan had changed his mind and would no longer let Fridrik marry her. At this point Fridrik also discovered that Natan had been sleeping with Sigga.
Natan then came back to the farm and told Fridrik to leave. Agnes slept in the cow shed that night and woke up to see Fridrik holding a hammer and knife. She went back to sleep and when she woke up she found Sigga cowering and Fridrik looking distressed. She entered the badstofa where she saw that Fridrik had killed Pétur and mortally wounded Natan. Agnes killed Natan with a knife because she knew he would die anyway. Then she and Fridrik burnt the farm with whale oil. Agnes’s side of the story wins Margrét’s sympathies.
Tóti wakes up from his illness one day to a letter saying that Agnes’s execution has been set. He rides to Kornsá to talk to Agnes, where Margrét tells him that Agnes told her the whole story. Agnes exchanges tearful goodbyes with the family at Kornsá and Tóti accompanies her to the place of her execution. Agnes and Fridrik are both executed as planned, with Tóti holding Agnes’s hand as she crosses the snow to the chopping block.