In the indictment, Roswall said the four should pay damages of $189,000, the minimum amount the men profited from the illegal activity, according to the prosecution.
Roswall said the men should also have their computers confiscated.
Swedish media reported that the four also risked up to a year in prison.
"It is very satisfactory that the prosecutor shares our opinion that Pirate Bay's activities are illegal. Sweden has received a reputation as a sanctuary for Internet pirates and that is not flattering," said Ludvig Werner, head of Ifpi, which represents the Swedish recording industry.
The Pirate Bay offices have been raided several times and shut down at least once by Swedish police.
The company provides instructions on how to skirt copyright fees and share music, film and computer game files using links offered on the site.
The site no longer provides numbers on how many downloads go through the site.
However, Henrik Ponten at Sweden's anti-piracy agency, said that between 15 and 24 million movies were illegally downloaded each year in the Scandinavian country alone.
"But music is the most popular thing to download," he said
Sweden, with just nine million inhabitants, is becoming a centre of piracy activity in Europe, said Ponten, as illegal file sharing sites facing closure in other European countries moved their activities there.
"When illegal file sharing decreases in Europe it increases in Sweden," he said, adding that he did not believe Thursday's indictment would change that trend.
He said: "The financial benefits are too big for them to just stop because of a trial."
Nine film files, including "Harry Potter and The Goblet of Fire" and the Johnny Cash biography "Walk The Line" as well as four computer game files are among the downloads cited in the charges.