This invention provides a polishing apparatus using a polishing material freely varying its shape in a tri-dimensional space in accordance with the shape of a work, and capable of polishing a narrow, recessed surface inaccessible to human hands or a tool, and a polishing method used therefor. A fluid containing grinding particles is solidified or gelatinized in accordance with the shape of a work; and the resulting solid body is moved relative to the work, thereby polishing or grinding the work. The fluid containing grinding particles is a magnetic fluid capable of controlling the orientation of grinding particles in the presence of a magnetic field; and the fluid is solidified or gelatinized while being exposed to a magnetic field. Alternatively, the grinding particles are dielectric grinding particles capable of polarizing in the presence of an electric field, and the fluid containing dielectric grinding particles is solidified or gelatinized while being exposed to an electric field. Further, a fluid containing grinding particles is poured on the surface of a work to be processed; and the fluid is solidified or gelatinized while it takes a shape in accordance with that of the surface of work to be processed, thereby producing a polishing material. A fluid containing grinding particles is solidified or gelatinized while it takes a shape in accordance with that of a work; and the resulting solid is moved relative to the work, thereby polishing or grinding the work.