A number of drivers called the police and reported seeing something on the road between junctions 20 and 21 of the M4 at 6.40pm on Saturday.
Police have discovered human remains on a motorway carriageway near Bristol and have shut parts of two motorways in both directions.
The M48 has also been closed both ways between junction 1 and the M4, and links from M5 to the M4 are also shut.
Avon and Somerset police officers attended and found human remains, which they believe are of a man in his 40s.
The closures, which are expected to cause significant delays in and out of Wales, are likely to remain in place until the early hours of Sunday morning, police said.
