Police arrested both men in the early hours of Saturday on Firth Park Road.
Police issued a statement this evening confirming the charges.
They said: “Two men have been charged after officers attended a Sheffield address yesterday (Saturday 14 May) responding to concerns over a safeguarding issue.
Andi Alushi and Valdemaras Kasinskas
“Andi Alushi, age 26, and Valdemaras Kasinskas, age 38, both of no known fixed address, have both been charged with two counts of kidnap, two counts of false imprisonment, two counts of arranging or facilitating the travel of another person with a view to exploitation, and a charge of Section 18 wounding.
“Officers attended an address on Firth Park Road at about 4.10am yesterday. Two men were found being held and are now receiving appropriate care.
“Alushi and Kasinskas have been remanded in custody and will appear before Sheffield Magistrates' Court tomorrow (Monday 16 May).”