The heritage trail aims to provide local people and visitors to the town an insight into the local fishing industry and its history.
The murals are proposed to be placed on the gable ends of 47 Flowergate and 84 Church Street.
The application from the council states: “We are proposing to fix two 16 square metre painted murals to two properties in Whitby
"The murals are on painted wooden boards and will be permanent fixings.
“One location is the gable end of Astin’s Estate Agents in Flowergate (facing westward up Flowergate towards Pannett Park) and the other is on the gable end of Hippy Hippy Shake in Church Street (facing South along Church Street towards Parkol).
“We have the permission of both building owners.
"Both murals are identical pictorial representations of a map of the Walk With Heritage sculpture trail.”
The sculptures include fisherwife, a man mending a net, a woman knitting a gansey, photographer and artist Frank Meadow Sutcliffe, a crow’s nest with a lookout, Dora Walker (the only woman to hold a skipper’s licence in the North Sea during World War One) and a herring lassie.
The mural application is now out for consultation.