The work investigated the effect of fatigue failure on the elastic characteristics of metastable austenitic steel AISI 321: Poisson’s ratio and acoustic anisotropy parameter. The elastic characteristics were calculated using ultrasonic measurements of the propagation time of longitudinal and shear elastic waves. The volume fraction of strain-induced martensite was determined by the eddy current method. Theoretical studies have shown that the main factors influencing Poisson’s ratio are the accumulation of microdamages and changes in phase composition. The change in the acoustic anisotropy parameter is associated with the influence of cyclic deformation on the crystallographic texture of the material matrix and the formation of oriented crystals of strain-induced martensite. Based on the analysis of experimental results, expressions were obtained for calculating damage and relative accumulated plastic deformation based on acoustic measurement data, which are widely used in engineering practice to determine the fatigue life of structural materials.