We report the axial strain dependence of two types of all-fiber acousto-optic tunable filters based on flexural and torsional acoustic waves. Experimental observation of the resonant wavelength shift under applied axial strain could be explained by theoretical consideration of the combination of acoustic and optical effects. We discuss the possibility of suppressing the strain effect in the filters, or conversely, the possibility of using the strain dependence for wavelength tuning or strain sensors.