Prosecutors say the victims were promised $500 a month, but instead were given little food or money for their 16-hour days cleaning stores and offices across the Mid-Atlantic.
Authorities say the Botsvynyuk (bots-VIN'-yuk) family operates a criminal racketeering enterprise.
Recruited villagers who tried to flee were beaten, raped or threatened, or had threats made against their families back home, Assistant U.S. Attorney Randall Hsia said.
"The defendants preyed upon their Ukrainian neighbors who were desperate to come to the United States," Hsia said in opening statements Monday morning. "You can't force someone to work for you against their will."
Five brothers are charged in the case, but only two, Omelyan and Stepan Botsvynyuk, are on trial. Two others are fighting extradition from Canada and one has died.
Defense lawyers said the men simply tried to offer opportunity to unemployed friends and neighbors who had come to them for help.
They suggested the witnesses are cooperating with the government only to get "the golden ticket" - a T-visa that lets trafficking victims settle in the United States.
"This is not the Corleone family," defense lawyer Howard Popper said, referring to the fictional Mafia family in "The Godfather" novel and movies. "You may find the Botsvynyuk brothers reprehensible. ... But the government has to prove a racketeering case."
The trial is expected to last more than a month, slowed in part by the need to translate some testimony. The government plans to call several former workers. They worked in crews cleaning Wal-Mart, Target and other retail stores, along with homes and offices in Pennsylvania, Maryland, Delaware, New York and New Jersey.