Abstract: A parabolic vibratory impact mill is proposed which comprises a housing having an outer cone, an inner cone and a power-operated vibrator. The shells of the cones have working surfaces in the form of parabolic generatrices: in the bottom part, the concavity of the parabolae is oriented toward the axis of the mill; in the top part, the convexity of the parabolae is oriented toward the axis of the mill. Conditions are created for the autogenous grinding of large pieces in the top part and small pieces in the bottom part, wherein the material partially decelerates in the transition region between the top parabolae and the bottom parabolae, providing for the metered feeding of the bottom region. The advantageous vertical distribution of the load in the grinding chamber provides a grinding ratio of 30 with little wear on the shells and low energy expenditure.