Police say road closures are in place at the Wingfield Road junctions with Brook Road and Bradford Road.
It follows the discovery in February of what is believed to have been phosphorus-containing incendiary devices from World War Two.
A 50m cordon is in place and local people have been advised to shut windows and doors.
Phosphorus grenades were issued to the Home Guard during World War Two.
The devices were used as improvised anti-tank weapons when Britain was facing possible invasion following the evacuation from Dunkirk.
In February, a cache of grenades were discovered in heavy clay soil at the site in Wingfield Road by builders.
The devices were destroyed in a controlled explosion.
The bomb squad has been called in after suspected anti-tank grenades were found on a building site in Trowbridge.