Damien Burns, 39, originally from Scarborough, North Yorkshire, and Dean Jackson, 27, from Newcastle, absconded from the category D Hatfield Prison yesterday evening, South Yorkshire Police said.
A force spokesman said: "Officers believe they may be attempting to make their way back to the areas they originate from as they do not have any known connections in the South Yorkshire region."
Burns was sentenced in 2007 and was serving an indeterminate sentence for a knifepoint robbery and Jackson was on remand awaiting a sentence for a theft-related matter, he said.
The spokesman said: "If seen, police would strongly advise the public not to approach either man but to make contact with South Yorkshire Police on 101, or Crimestoppers anonymously on 0800 555111, quoting incident number 1009 or 1067 of 19 May 2014."
The incident comes a day after a murderer who stabbed a blind man to death was arrested after going on the run from prison.
Arnold Pickering was arrested for being unlawfully at large at an address in Oldham.
The 44-year-old, who was jailed for life in 1991 for killing a man he wrongly thought to be a paedophile, failed to return to HMP Kennet in Merseyside after leaving the Category C jail on day release on Saturday.
Another inmate, swastika-tattooed Thomas Moffett, 51, who is serving an indeterminate sentence for a number of robberies, also failed to return from day release on Saturday, but was arrested last night for being unlawfully at large.
These incidents came just two weeks after notorious armed robber Michael Wheatley - known as Skullcracker - absconded from Standford Hill open prison on the Isle of Sheppey, Kent, while on temporary release.