A 37-year-old man found dead in a field near Hull suffered an "horrific and agonising death", police have said.
Mr Callaghan was kicked, punched and struck with an implement
Stephen John Callaghan, of Elloughton Grove, Hull, was brutally beaten to death "in a very cruel way". He had also been shot with an air weapon.
His body was found on Wednesday near a railway line between Hornbeam Drive and Snuff Mill Lane, Cottingham, by a man walking his dog.
Police are continuing to question two teenagers arrested on Wednesday night.
A spokeswoman for Humberside Police said magistrates had granted detectives an additional 25 hours in which to detain and question the 17-year-old Cottingham boy and 18-year-old man from Hull.
A 15-year-old boy, who was also arrested on Wednesday, has been released on bail until February 2007.
The spokeswoman said police had received 30 calls from people about the incident on Thursday but appealed for anyone else with information to contact them.
Mr Callaghan, who lived with his parents, was last seen when he left his family home at 1500 GMT on Boxing Day. He was unmarried and had no children.
He was known to have visited the Snuff Mill Lane area quite regularly, and police said they were now trying to piece together his last movements.
Mr Callaghan was last seen at his home on Boxing Day
Post-mortem tests carried out on Wednesday revealed Mr Callaghan suffered severe bruising across his body.
It is thought he had been kicked, punched and struck with an implement.
Det Supt Ray Higgins said: "This man died an horrific and agonising death and sustained horrendous injuries.
"He was brutally beaten to death in a very cruel way and it is vital that anyone who knows anything about the circumstances surrounding his death contact police urgently."
Mr Higgins said police also wanted to speak to people with information about air weapons being used in the area and speak to dog walkers who may have information about where the body was found.
An anonymous caller who contacted police with "interesting" information on Wednesday has got back in touch with detectives following an appeal.