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One embodiment of the present invention relates to a method for extracting rare metal elements, comprising : a first step of preparing an extraction filtrate by reacting coal ash and an extraction solvent, which includes a halogen acid; and a second step of adding a non-halogen acid extraction solvent to the extraction filtrate, and applying an ultrasonic vibration heat source thereto and reacting the same. Therefore, the present invention can extract, with high efficiency, yttrium (Y), neodymium (Nd) and gallium (Ga) from coal ash, which is a waste product of electric power.