A method of forming a material includes the steps of: vibrating a molten material at an ultrasonic frequency while cooling the material to a semi-solid state to form non-dendritic grains therein; forming the semi-solid material into a desired shape; and cooling the material to a solid state. The method makes semi-solid castings directly from molten materials (usually a metal), produces grain size usually in the range of smaller than 50 μm, and can be easily retrofitted into existing conventional forming machine.