The invention relates to a grinding body for crushing and grinding of ores rocks or earth, inert and all other materials, in drum and other mills. It finds application in ore enrichment, production of construction materials, waste processing and other industrial branches. The grinding body comprises a spheroidal cone (1), whose forming curve (5) is part of a circle or of some other geometrical curve and a vertex (6), and a base (2) which is part of a sphere or of other three-dimensional figure, obtained by rotation of geometrical curves and an edge (4) between them. In one of the versions the cone (1) and the base (2) are connected by a cylinder (9). For better producibility of the grinding body, a flat spot (3) with circular or other shape is made on the surface of the base (2). In another version the flat spots (7, 8) are made on the surface of the cone (1) and on the surface of the cylinder (9) between the base (2) and the cone (1). In a subsequent version the vertex (6a) of the cone (1) is cut flat with its plane perpendicular or inclined towards the axis of the body. In other versions, more or less convex peripheral rings (10, 11, 12) are made between the cone (1) and the base (2). The cross section of these rings has the shape resembling a circle, a triangle or a rectangle. In a subsequent version on the base (2) and on the flat cut vertex (6a) short cylinders (13) with flat bases (14) are protruding. All edges and the vertex of the body may be rounded along part of a circle, spiral or other geometrical figure. The grinding body has greater area than the spherical grinding body and greater density in a given space. The existence of an edge and a vertex increases milling productivity.