Various scribbles and words, including offensive language, have been daubed over two bridges over the past three to four weeks.
Police are also concerned that the suspects are risking their lives by crossing exposed girders to reach the underneath of the bridges.
Names including Booki, Nook and Salaz have been included in the graffiti and officers hope someone may recognise them and come forward with information that could assist the investigation.
Anyone with any information is asked to contact North Yorkshire Police on 101, select option 2 and ask for Philip Wright. Or email firstname.lastname@example.org
If you wish to remain anonymous, you can pass information to Crimestoppers on 0800 555 111.
Please quote reference 12180090279 when passing on information.