Abstract: Solid particulate material such as cement raw material, clinker, etc., is finely ground, crushed or pulverized, by means of a rotatable generally vertically oriented container of generally inverted frusto-conical shape, and having grinding media such as steel balls disposed therein. The discrete particles of the material to be pulverized are fed into the upper part of the container as it is rotated about a central vertical axis, and egress of the resulting finely ground material by centrifugal force from the container to external collection is accomplished by the provision of slits in the inclined side wall of the rotary container. A fixed cover enclosing the upper part of the container is provided with inner guide vanes which are typically curved or of a vortical form. A preliminary coarse crushing mechanism may be provided, and this mechanism may be integrated with the rotary container, so that coarse crushing and fine crushing may be performed by a single device.