A multi-chamber inclined ball mill comprises a base, a frame-shaped support member rotatably supported on the base, and a grinding chamber rotatably supported on the frame-shaped support member. The grinding chamber is constituted of at least three cylindrical chambers each provided with outwardly tapered protrusions at its opposite ends and the cylindrical chambers integrally formed so that their longitudinal axes mutually intersect at the centers thereof and form a common grinding space at their region of intersection. The grinding chamber is supported on the frame-shaped support member such that the longitudinal axes of the cylindrical chambers intersect the axis of rotation of the frame-shaped support member at a single point and at one and the same angle.