The ring compression test has been widely employed as an experimental means to determine the friction factor. The calibration curves are obtained by the rigid-plastic finite element analysis for various work-hardening exponent and strain-rate hardening exponent. The effects of work-hardening exponent and strain-rate hardening exponent are thoroughly studied and discussed from the finite element computation. The change of friction factor during height reduction in ring compression is also discussed. Then, the method to estimate the change of friction factor during ring compression is proposed.