Officers attended the incident in the New Road area at approximately 9.30pm on June 3.
A 16-year-old male was taken to hospital with serious injuries.
A 17-year-old male from Royal Wootton Bassett and a 17-year-old male from Swindon have since been charged with possession of a knife blade in a public place and section 18 GBH with intent.
They have been remanded in custody and are due to appear in Swindon Magistrates Court today. (5/6)