To provide sufficient impact absorbability to the connection part of a valve element in a swing valve and a swing arm.

A method for manufacturing the valve element in the swing valve includes: a polygonal column forming step S10 of obtaining a polygonal column 130 formed of a heat-resistant steel by executing swaging and cogging of a steel block 100 of heat-resistant steel which is the base stock of a valve element 20; a stepped body forming step S20 of obtaining a stepped body 140 having a small diameter section 140b formed by executing tap forging of an end of the polygonal column and a large diameter section 140a; a disk-with-projection forming step S30 of obtaining a disk 150 with a projection by inserting the small diameter section in the stepped body in a hole 510 in a hole base 500, and swaging the stepped boy in its axial direction Z; and a machine-forming step S40 for machine-forming the disk with the projection so that a projection part 20b is formed from the small diameter part 150b in the disk with the projection, and a body 20a is formed from the large diameter part 150a.