Andi Alushi, 26, and Valdemaras Kasinskas, 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 4.00am on Saturday.
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 on Monday.