New York City schools will start vaccinating students against swine flu next week.

Mayor Michael Bloomberg is urging parents to sign the consent forms that are going home with schoolchildren.

Bloomberg joined Schools Chancellor Joel Klein and Health Commissioner Thomas Farley on Tuesday for a news conference about the vaccination program.

They said the swine flu vaccine will be offered for free at all city elementary schools — public and private — starting Oct. 28.

Farley said he expects to have enough vaccine for all of the schools.

Bloomberg said parents can have their children vaccinated at a doctor’s office or a clinic if they prefer.