A group of workers started to demolish unoccupied tents and shacks by hand, according to reporters at the scene.
About 2,000 migrants left voluntarily on Monday, and hundreds more have followed on day two of the clearance.
The Jungle has become a key symbol of Europe’s migration crisis, housing some 7,000 residents in squalid conditions.
The operation to close the camp has been largely peaceful so far, but concerns remain that some migrants will refuse to give up their attempts to cross the Channel to the UK.
The French authorities said they were prioritising departures on Tuesday morning, but crews in hard hats and orange jumpsuits started demolition shortly after 1500 local time (1400 BST).
They tore down wooden shacks with sledgehammers and used diggers to move away debris.
The demolition is expected to be done mostly by hand – and in a low-key manner – as officials believe sending in bulldozers at this point would send the wrong message to migrants they want to convince to get on buses voluntarily.
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