The DCO application seeks permission for number of changes to the A303 between the town of Amesbury and Berwick Down.
The existing single carriageway road runs through the Stonehenge World Heritage Site, just 165 metres away from the stone circle.
Highways England has proposed upgrading the road to a dual carriageway and placing a section of it close to the Stonehenge within a 1.8-mile tunnel.
The agency said a new road tunnel will "help unlock economic growth in the South West by improving journey reliability, increasing safety and improving connectivity with neighbouring regions, while protecting and enhancing the environment".
PINS has until Friday 16 November 2018 to decide whether to accept the application for examination.
If accepted, public examination would take place early next year and construction work could begin in 2021. More details on the application can be found here.
In August, the agency submitted plans for the creation of a dual carriageway on another section of the A303 north of Yeovil.