Sizwe Bansi Is Dead begins in the photography studio of a man named Styles, situated in New Brighton, Port Elizabeth, South Africa. After reading a newspaper article about an automobile plant, Styles shares a humorous anecdote with the audience about an incident that happened when he worked at Ford Motor Company.

As Styles continues to read the newspaper, he talks about his photography business. His musings are interrupted by the arrival of a customer, Sizwe Bansi, who wants his picture taken. When Styles asks for a deposit and Sizwe's name, Sizwe hesitates and then says his name is Robert Zwelinzima. Styles inquires about the purpose of the photo, and Sizwe explains that he intends to send it to his wife. Once the picture is taken, the moment captured in the photograph comes to life, and Sizwe begins dictating a letter to his wife that will accompany the photo.

In the letter, Sizwe informs his wife that Sizwe Bansi is dead. He recounts how, after arriving in Port Elizabeth from their home in King William’s Town, he stayed with a friend named Zola who tried to help him find employment. Despite their efforts, Sizwe's job search was unsuccessful, and he was ordered by authorities to leave within three days. Consequently, Sizwe went to stay with Zola’s friend, Buntu.

The play then returns to the present time. While staying at Buntu’s house, Sizwe shares his predicament with Buntu, explaining that unless a miracle happens, he will have to leave town in three days. Buntu, understanding the gravity of the situation, suggests that Sizwe work in the mines in King William’s Town. Sizwe dismisses this idea as too dangerous. In an attempt to lift Sizwe’s spirits, Buntu decides to take him to a local bar called Sky’s place.

The narrative shifts back to Sizwe as he continues writing the letter to his wife. He describes his experiences at Sky’s Shebeen, where he was served alcohol by a woman in a respectful manner.

Sizwe Bansi Is Dead transitions to the exterior of Sky’s bar after Sizwe and Buntu have been drinking. Buntu realizes he needs to get home for work the next day. He goes into an alley to relieve himself and discovers a dead man. Sizwe wants to inform the police about the body, but Buntu dismisses the idea. Instead, he retrieves the dead man’s identity book to find his address. The deceased man, Robert Zwelinzima, possesses a work-seeker’s permit—the very thing Sizwe needs to remain in town. They decide to take the book.

At Buntu’s house, Buntu switches the photographs in the identity books. He suggests they burn Sizwe’s book, effectively making him "dead," and have Sizwe assume the dead man’s identity to stay in Port Elizabeth. Sizwe is hesitant about the plan, particularly concerned about his wife and children. Buntu argues that they can remarry. After extensive discussion, Sizwe agrees to the switch.

Sizwe finishes dictating a letter to his wife, explaining that Buntu is assisting him in obtaining a lodger’s permit. The scene then shifts back to Styles’ photography studio, where Sizwe is having his picture taken.