Police consider the pair dangerous and have warned the public not to approach, Lauititi Tualima and Aniseko Vaelei, who escaped early yesterday morning.
The pair are serving time for a number of offences including robbery, rape, burglary and theft.
The new multi-million dollar prison has a high security fence but work is still underway for its completion. The prison was opened in June.
Meanwhile, one of the men, Lauititi Tualima, had also escaped from the old Tafaigata prison and while on the run raped an Australian tourist.
The other prisoner, Aniseko Vaelei, also escaped from Tafaigata early this year with another inmate, Pati Chong Nee.
Vaelei and Nee robbed a Chinese couple who run a supermarket and stole US$27,000 in cash.
The police had managed to arrest Vaelei but Nee is still on the run.