Torp had a cerebral haemorrhage in the early 1950s, which he kept secret to most his acquaintances, even family. On 1 May 1958 he had a new cerebral haemorrhage, this time with a fatal outcome. He died at Rikshospitalet. This was May Day, and Torp was scheduled as the main speaker in Stavanger. He was not able to do it, and thus, Arne Skaug read Torp's manuscript. When the speech was referred to in the newspapers the next day, it was accompanied by obituaries of Torp. He was buried at Vår Frelsers gravlund. A memorial stone was raised in Skjeberg in 1976.

Books about Torp include Nils Hønsvald's Oscar Torp, released in 1959, and Egil Helle's Oscar Torp – arbeidergutt og statsmann, released in 1983. In 2007 Hans Olav Lahlum released Oscar Torp. En politisk biografi.