To provide an electron beam assisted EEM method that can realize ultraprecision machining of workpieces, including glass ceramic materials, in which at least two component materials different from each other in machining speed in a machining process are present in a refined mixed state and the surface state is not even, to a surface roughness of 0.2 to 0.05 nm RMS. The EEM method comprises a working process in which a workpiece and chemically reactive fine particles are allowed to flow along the working face to remove atoms on the working face chemically bonded to the fine particles together with the fine particles through chemical interaction between the fine particles and the working face interface. The workpiece comprises at least two component materials present in a refined mixed state and different from each other in machining speed in the machining process. After the exposure of the workpiece in its working face to an electron beam to conduct modification so that the machining speed of the surface layer part in the working face is substantially even, ultraprecision smoothening is carried out by working process.