Sweden's Justice Ombudsman has received a letter from the Prisoners' Council at Sagsjön jail in which the women bemoan the fact that they are not permitted to wear bikinis.
"It's a human right," wrote the chairwoman of the council.
Since bikinis are not standard issue in jail, and inmates are not permitted to wear their civilian clothes, the prisoners consider themselves victims of discrimination, Aftonbladet reports.
"How are we supposed to be able to sunbathe at all? They answer we have got is that we can sunbathe in shorts and sports tops.
"In other words, we are treated differently because we are in an institution and we are disriminated against because of our gender," the women wrote.
"We want to be able to enjoy the sun just like everybody else in Sweden, whether they are in an institution or on the outside."