We investigate in detail the origin of multiple resonance peaks experimentally observed in an all-fiber acousto-optic tunable filter built with a photonic crystal fiber having slightly deformed air-hole structure and non-circular outer cladding. A model for the acousto-optic mode coupling in the PCF is formulated taking into account both the acoustic and the optical birefringence. All experimental results are in good agreement with numerical calculations. (c) 2008 Optical Society of America.