SKDC's Environmental Health Team and the Environment Agency are working together during the clean-up operation to secure evidence which it is hoped will lead to the offender.
Anyone with information is asked to contact the council on 01476 406080 or the police on their non-emergency number, 101.
Cabinet Member for Commercial and Operations, Cllr Dr Peter Moseley, said "This is the largest fly-tip I have ever seen.
"It is an example of appalling antisocial behaviour and disrespect for both our environment and local residents.
"If we can bring people to account for this despicable act against our countryside, I hope the legal process will support our aim to stamp this out by issuing the most severe penalty available.
"Someone may have seen something, so I ask anyone who has passed through to think back and let us know so that we can take steps to prevent this sort of behaviour.
"Please be vigilant. If you see something suspicious, then report it or we could see more of the same."
SKDC also urges anyone using a waste carrier to check that they are legal and registered by calling the Environment Agency on 03708 506506 or visiting https://bit.ly/check-waste-carrier