A caravan and a catering van were set on fire in Kirkcaldy, resulting in damage worth £15,000.
Police say the blaze completely destroyed the trailers, which were stored in a yard near Torbain Tower.
The wilful fire raising happened in a rural area between Friday August 20 and Friday August 27.
Detective Constable Donald McGarva said: “Although this is a rural area, it can easily be accessed from the Newliston area of Kirkcaldy.
“I would appeal to anyone who saw anything suspicious, or who has any information that may assist our ongoing enquiry to contact officers through 101 with reference 3603 of August 27.
“Alternatively Crimestoppers may be contacted on 0800 555 111, where anonymity can be maintained.”