Qualitative comparison of the effect of ultrasonic treatment and annealing on the structural relaxation of a two-dimensional nanocrystalline material after severe plastic deformation has been performed by the molecular-dynamics method. The treatments of both types lead to a decrease in the dislocation density and to a more equilibrium state of grain boundaries and triple junctions but, unlike the temperature effect, ultrasonic treatment does not result in a considerable grain growth. Thus, the calculations conducted indicate potentialities of the ultrasonic treatment of bulk nanomaterials with the aim of relieving internal stresses without increasing grain size.