Don Valley MP Caroline Flint has demanded an enquiry into the escapes from Hatfield Open Prison.
Damien Burns, 39, originally from Scarborough in North Yorkshire, and Dean Jackson, 27, from Newcastle-upon-Tyne, absconded from the open prison on Monday and are still on the run.
Ms Flint, whose constituency includes Hatfield Open Prison, said: “It is extraordinary that an offender serving a term for a violent knife offence is in an open prison. And I’m also concerned about whether an open prison is the right place for remand prisoners who have been refused bail.
“This raises the whole question of how secure our prison system is. These are not the first escapes, and it is not the first time that serious offenders appear to be have been put in low security prisons.”
“Open prisons have a valuable contribution to make, but are undermined if the wrong class of inmates are placed there.”
The MP will be raising the matter with the Justice Secretary when Parliament returns.
Police are asking the public for assistance in locating the two men - but are urging people not to approach them.
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 serving an indeterminate sentence, since 2007, for a knifepoint robbery and Jackson was on remand awaiting a sentence for a theft related matter.
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.