An electromagnetic stirring apparatus includes a vessel (2) for containing an electroconductive material in a molten state, such as a molten metal (1); an axially traveling magnetic field generating coil (3) for generating magnetic line of force (15) in an axial direction of the vessel (2) towards the molten metal (1) contained in the vessel (2) from an outside of the vessel (2); and a strip-shaped magnetic plate (4) disposed between the coil (3) and the vessel (2). Portions (11) where an axial electromagnetic force is generated in the molten metal contained in the vessel by the coil (3), and portions (10) into which a magnetic field is prevented by the magnetic plate (4) from locally entering, are formed in the vessel (2), whereby a circumferential pressure gradient is generated. Only with the axially traveling magnetic field generating coil (3), streams formed by convolution of axial motion and rotary motion are generated in the molten metal (1) in accordance with the axial electromagnetic force and the circumferential pressure gradient, thereby to perform stirring of the molten metal (1).