Mr Tyndall, from Llantwit Major, was last seen at 12.40am near the medical center in the direction of Boverton Road.
Police are concerned for their welfare.
The 31-year-old is described as 5ft 7in, with dark short hair and a dark beard. He has a lion tattoo on his upper right arm with the name Daniel. He was last seen wearing a black hoodie, blue jeans and black shoes.
Anyone with information on their whereabouts can call 101 or send South Wales Police a direct message on Facebook or X quoting 2300395878.
A spokesperson for South Wales Police said: “We are appealing for information to find Rhys Tyndell who has been reported as missing.
“Rhys, 31, was last seen at 12.30 am this morning (Tuesday, November 21) wearing a black hoodie, blue jeans and black shoes and officers and concerned for his welfare.
“At 12.40 am, CCTV shows a man matching Rhys’ description near the medical center running in the direction of Boverton Road.
“Rhys is described as 5ft 7in tall, with dark short hair and a dark beard. He has a lion tattoo on his right upper arm with the name Daniel.
“Anyone who has seen Rhys or has information which might help us find him is asked to please contact us by one of the following means quoting 2300395878.”