As a highlight of the year-long York 800 programme, the dig is taking place in the Guildhall yard, the basements of the Mansion House, Common Hall Lane and the south side of the Guildhall.
The 2012 events mark the 800 years since the city was granted a Royal Charter by King John in 1212, allowing York to take charge of its own affairs by electing a council, creating the post of mayor, and giving its people a voice.
The York Archaeological Trust went onto the site on Monday for six weeks.
And, the organisers say, any significant finds will be displayed in the Mansion House.
Councillor Sonja Crisp, York Council cabinet member for leisure, culture and tourism, said: “In this year of York 800, it seems very fitting that we can host a dig at the principal seat of local democracy in the city.
“I’m very excited at the prospects of what might be found on the site.”
The dig is open to the public at set times next week as part of York’s Medieval Summer, when visitors can meet Trust members the archaeologists, and see finds as they are documented.
Visitors can also see the recent vertical survey and imaging of the Guildhall which was carried out by the Trust.
The first Guildhall in York is mentioned in 1256 in a charter given to citizens by King Henry III.
From 1378 onwards, records indicate a Guildhall on the present site.
The dig aims to establish the dates of the basements of the Mansion House, land levels around the Guildhall and river frontages, which could hold well -preserved waterlogged deposits.
Diggers may also detect structures that existed in the Guildhall yard and adjoining areas such as kitchens, a brew house, and stables, and to date evidence that establishes the sequence in which the area developed.