One carcass was seen floating near Staithes and Sandsend, beginning to decompose and bloat. Two others had beached, already dead, close to Whitby’s piers with nets still around them.
Footage posted online showed one having to be dragged away by a tractor.
The animals – minke whales – were spotted on Tuesday by passengers aboard a Whitby Whale Watching vessel.
Such creatures are now a regular sight off the Yorkshire coast, where they can be seen following shoals of herring through the North Sea in the summer months.
Ryan Chadwick, a wildlife artist who was aboard the tourist boat, said: “We had seen 50 bottlenose dolphins on the trip, but everyone was just so depressed by the sight of the whale."
He said it was believed the animals had become entangled in the lobster pot chains, vast heavy-duty trammels set up by local fishermen which run from pots on the seabed up to buoys on the surface.
Speaking to the Yorkshire Post, Mr Chadwick added: “We were about 15 miles out when we saw it…
“We think it had only been dead for about two hours, as it hadn't swollen up. The mother was nearby and she was swimming around and blowing in distress.
"Two more were later found, one rotting near Whitby Pier with fishing line around its neck. The other looked like lobster pot wire. The skipper thought one of them might end up beaching in the Runswick Bay area, judging by the direction it was drifting.”
At least three other whales have been killed in separate incidents involving fishing gear off the Yorkshire coast in the past decade.