The fluid inertia effect on the behavior of an elastic ring squeeze film damper (ERSFD) becomes significant at high whirl frequencies. However, the existing literature on the ERSFD lacks a comprehensive lubrication model concerning the fluid inertia. This study aims to establish a lubrication model for the ERSFD taking into account the inertia effect with using the average velocity method. The temporal and convective inertia effects on the inner oil film force are analyzed under different operating conditions. The result shows that the temporal and convective inertias should be considered for the modeling of ERSFD, especially at large eccentricity ratios or high whirl frequencies; the oil film force of the ERSFD with the attitude angle exhibits a unique periodicity due to the action of bosses. This study is the first comprehensive investigation on how the temporal and convective inertias affect the ERSFD's behavior.