We propose a novel model of the acousto-optic interaction in circular fibers endowed with the lowest-order flexural acoustic wave that is based on the actual distribution of the acoustically induced displacement vector. The corresponding expression for the fiber's permittivity is derived and compared with the commonly used one. The resonance optical fiber modes and the propagation constants are found. It is predicted that the lengths of the well-known acoustically driven mode conversion LP0,n→LP1,n' should be slightly different for the x- and y-polarized incident fundamental modes. Moreover, we unveil a new polarization-dependent mode conversion in which the azimuthal mode number ℓ, as well as the optical frequency of the generated standard fiber mode LPℓ,n' , is governed by the linear polarization direction of the incident zero-order beam LP0,n.