Vessel collisions pose significant threats on the safety of cross-channel bridges. Previous studies have paid little attention on the impact performance of common arch bridges with gravity foundations in inland waterways. This study aims to comprehensively investigate the anti-impact resistance and analyze the damage and failure mechanisms of arch bridges under vessel collisions. The entire process of vessel-bridge collision is simulated using three-dimensional explicit finite element technique. The damage characteristics, as well as the progressive collapse process of arch bridge are investigated thoroughly. Moreover, the rational calculation method for bridge lateral resistance against vessel collisions (BRaVC) is discussed. The results show that the gravity foundation bottom section of arch bridge can be fixed in vessel-bridge collision numerical analysis due to insignificant foundation-soil interaction. The head-on barge collision on the bridge pier leads to indistinctive lateral displacement, while obvious local damage can be observed. The impact displacement of the bridge pier is not positively correlated with the impact energy according to the impact load spectra analysis. Barge collision on the main arch results in the progressive collapse of the bridge due to unbalanced horizontal thrust from the arch on the other side. The rational BRaVC can be calculated by using sectional strength based on elastoplastic section analysis.