The magnetic fields on the beam axis of helical undulators for the proposed International Linear Collider (ILC) gamma-ray production were calculated for undulator periods of 10 mm and 12 mm. The calculation assumed the use of low-carbon steel for the magnetic poles and a beam chamber outer diameter of 6.3 mm. Using NbTi superconducting coils at 4.2 K, the on-axis field for a 10-mm-period undulator was 0.62 T at the critical current density. The field for a 12-mm undulator period was 0.95 T, which gives a K value of 1.06. The K value for an 11-mm undulator with Nb{sub 3}Sn superconducting coils was estimated to about 1.1.