We show that a bending mechanical stress can produce a topological defect of orientation of the eigenvectors of Christoffel tensor with the strength equal to ½. This implies generation of a singly charged acoustic vortex for transverse acoustic waves. In general, this vortex is anisotropic, although it can be transformed into isotropic one at some geometrical parameters of distributed mechanical load. The acoustic vortices generated by the bending stresses can be produced even in isotropic solid-state media. Using the example of crystals belonging to the point symmetry group 3m, we also consider the process of backward collinear acousto-optic diffraction for the case of interactions of optical and acoustic waves that bear bending-generated topological defects of their phase fronts. It is demonstrated that, in the case of linearly polarized incident optical wave, a vector beam with a unit polarization order is generated in the crystals. Acousto-optic interaction of this vector beam with the acoustic beam bearing a singly charged anisotropic vortex produces a diffracted optical wave that bears a vortex, too. The embedded topological defect of the phase front associated with this vortex has the strength given by a sum of strengths of the topological defects of the incident optical wave and the acoustic wave. The diffracted optical beam represents an anisotropic vortex beam with the orbital angular momentum (OAM) equal to 2ħ. When both the acoustic wave and the incident optical wave nest the bending-induced singly charged anisotropic vortices, the diffracted optical wave would also bear a vortex. Its charge is a linear combination of the charges referred to the acoustic and incident optical waves, which involves the parameters of acoustic and optical anisotropies. When the signs of OAMs of the interacting acoustic and optical waves are the same, the diffracted optical wave bears a doubly charged anisotropic optical vortex. At some specific anisotropy parameters, it can be transformed into isotropic vortex. Finally, the topological defects embedded in the interacting waves annihilate and the diffracted optical wave becomes vortex-free when the signs of OAMs of the interacting waves are opposite.