Report by Amelia Beckett
It comes as a lack of abattoir workers meant 10,000 pigs were culled in the region in the run-up to Christmas.
Without abattoirs to process the pigs, farms simply run out of space to keep them, resulting in the culls.
East Riding of Yorkshire Council was told those staff shortages were fuelled by Brexit, with many workers returning to their home countries.
Sisters Kate Moore and Vicky Scott, who run a pig farm in Driffield, have called the action "criminal."
Kate said: "It's a disgrace that 35,000 across Great Britain have been killed on farm and wasted. It's a complete waste. It's criminal what has happened."
The sisters would normally sell around 90,000 pigs a year. They are contracted to a certain number of pigs to go to slaughter every week. But currently those contracts are not being taken due to the staff shortages. They are down 30%, losing between £25 to £30 per pig.
"We're the ones who are suffering financially and emotionally. The farmers are taking the hit in every way", said Vicky.
"We are suffering massively through no fault of our own and the government have to be held responsible for that."
In October the government stepped in to try and increase staffing levels by offering seasonal worker visas to EU butchers, allowing them to stay in the UK for up to six months.
They said eight hundred workers should be enough to deal with the crisis, but delays due to concerns over the Omicron variant mean many still haven't arrived.
Conservative councillor Charlie Dewhirst, who also works for the National Pig Association, said the measures had not worked and farmers are on the verge of being forced out of business.
"If this goes on any longer, we'll see more and more farms go out of business. That in turn affects all the indirect business that support farms here in the East Riding.
"It's a hugely important part of our rural economy and ultimately we won't have an industry left in the UK."
East Riding of Yorkshire Council have now backed a motion calling on the Conservative-run authority to write to the government raising concerns for farmers and calling for an inquiry into the shortages.
The Department for Environment, Food and Rural Affairs said it remains in close contact with industry and stakeholders to discuss the challenges facing the pig sector.
It added it was paying abattoirs to slaughter more pigs and hiring cold storage facilities to store the carcasses.
As for Kate and Vicky, they said they would rather close their second generation farm than let any of these pigs go to waste.