A porbeagle of approximately eight feet in length was reeled in on the Whitby vessel Sea Spray, followed by another smaller shark, which was around six feet long.
Malcolm Pitman of the boat Sea Spray and Richard Ward of Shy Torque, have both been fishing for sharks from Whitby for several years now.
They also participate in the National Shark Tagging Programme, which is an important exercise as so little is known about these huge fish.
Whenever possible, measurements are taken and the fish is then tagged and released safely. The crew also reported seeing an even larger shark before the first shark took the bait.
Tagging programmes with various species of shark produce valuable data for the development of fisheries management.
The programme is aimed at sport shark anglers who record, tag and release the sharks that they catch.
Porbeagle sharks tend to be found in waters around the UK, usually at least 10 miles out to sea.
Despite their monstrous appearance, they are not thought to pose a danger to human beings.