"It's not about having the prisoners and their needs in focus. It's about having their children's needs in focus," said Eva-Karin Eriksson, children's officer at the Swedish Prison and Probation Service (Kriminalvården).
The project is called "Goodnight stories from the inside", which the library and the prisons service hopes will become a permanent part of prison life.
The inspiration for the project comes from Britain, where there is a similar project called "storybook dads". The prisons service is hoping to expand the project to all institutions across Sweden.
The idea is to strengthen the bonds between inmates and their children and families. The reading project has been enthusiastically received by the 60 or so inmates who have so far taken part, and also among their relatives.
At best, the project could lead to fewer repeat offenders, hopes Eva-Karin Eriksson.
"One can imagine that if family relationships are made stronger then there is more to lose by going to prison again."
Study circles have been held in prisons in Malmö with prisoners recording the stories onto CD. Prisoners sometimes also sketch illustrations to cover the discs.
"There are even those that have sung lullabies to their children," said Eriksson.