A method of manufacturing a cylindrical ring member (18; 20) comprising: a step of forming a metal intermediate material having a cylindrical portion (46; 47); and a chamfering step by cold forging in which a normal chamfer portion (61; 62) is formed on an axial end peripheral edge of the cylindrical portion (46; 47) by pressing a radial end portion of an axial end surface of the cylindrical portion (46; 47) against an annular chamfering surface (60; 73) provided in a mold configuring a mold device, wherein the mold device further includes a second mold having a ring-shaped holding surface arranged coaxially with the chamfering surface of the mold and adjacent to the chamfering surface (60; 73) of the mold in a radial direction, wherein the chamfering step by cold forging is performed by pressing the radial end portion of the axial end surface of the cylindrical portion (46; 47) in an axial direction against the chamfering surface (60; 73), and pressing a portion, which is adjacent to the radial end portion in the radial direction, of the axial end surface of the cylindrical portion (46; 47) in the axial direction against the holding surface, characterized in that when performing the chamfering step by cold forging, the holding surface is initially brought into contact with a radial intermediate portion of the axial end surface of the cylindrical portion (46; 47), and that a chamfering step is performed by cold forging in a state where a preliminary chamfer portion (36; 37), of which a width dimension in a radial direction is larger than a width dimension of the normal chamfer portion in a radial direction, is formed on the axial end peripheral edge of the cylindrical portion (46; 47). a step of forming a metal intermediate material having a cylindrical portion (46; 47); and a chamfering step by cold forging in which a normal chamfer portion (61; 62) is formed on an axial end peripheral edge of the cylindrical portion (46; 47) by pressing a radial end portion of an axial end surface of the cylindrical portion (46; 47) against an annular chamfering surface (60; 73) provided in a mold configuring a mold device, wherein the mold device further includes a second mold having a ring-shaped holding surface arranged coaxially with the chamfering surface of the mold and adjacent to the chamfering surface (60; 73) of the mold in a radial direction, wherein the chamfering step by cold forging is performed by pressing the radial end portion of the axial end surface of the cylindrical portion (46; 47) in an axial direction against the chamfering surface (60; 73), and pressing a portion, which is adjacent to the radial end portion in the radial direction, of the axial end surface of the cylindrical portion (46; 47) in the axial direction against the holding surface, characterized in that when performing the chamfering step by cold forging, the holding surface is initially brought into contact with a radial intermediate portion of the axial end surface of the cylindrical portion (46; 47), and that a chamfering step is performed by cold forging in a state where a preliminary chamfer portion (36; 37), of which a width dimension in a radial direction is larger than a width dimension of the normal chamfer portion in a radial direction, is formed on the axial end peripheral edge of the cylindrical portion (46; 47).