The invention intends to provide an apparatus for generating compression waves in a conductive liquid, which sufficiently enhances a strength of the compression waves by improving an ac electromagnetic force applying means that generates the compression waves directly in the conductive liquid contained in a vessel. To accomplish the object, the apparatus of the invention comprises a vessel containing a conductive liquid such as a molten metal and an ac electromagnetic force applying means provided around the circumference of the vessel, which generates the compression waves in the conductive liquid contained in the vessel to thereby achieve material improvement after the solidification of the conductive liquid. The ac frequency f of the ac applying means is set within a range given by the following Äexpression 1Ü, for a strong generation of the compression waves: 2 DIVIDED L pi mu sigma mu sigma DIVIDED 2 pi here, f: frequency (a major frequency when a wave-form of an electromagnetic force is developed by the Fourier transform, in case of the wave-form being a non-sine wave) L: characteristic length of the system (for example, a depth, a radius of the vessel containing the conductive liquid) mu : permeability of the conductive liquid sigma : electric conductivity of the conductive liquid c: propagation velocity of the compression waves in the conductive liquid.