The hinge type of precast concrete arch culvert was introduced to Japan from France in the 1990s in consideration of the saving of labor, shortening of the construction period, and high quality control of the concrete members. However, due to the 2011 off the Pacific Coast of Tohoku Earthquake (March 11, 2011), the three-hinged precast arch culverts that had been constructed in Japan at the beginning of the period when precast arch culverts were firstly introduced, suffered damage, which spoiled their serviceability. According to the extent of the damage and the type of culverts that were damaged, the longitudinal structural connectivity of the culverts was assumed to be one of the possible reasons for the reported damage mechanism. Therefore, the objective of this paper was to clarify how strongly the longitudinal structural connectivity influenced the longitudinal seismic behavior of the three-hinged arch culverts. To achieve this objective, an elasto-plastic finite element analysis was conducted with an analytical model that could capture the characteristics of the damaged culverts. Simultaneously, a penalty method with the bi-linear spring model was applied as a solution to the contact-impact problems of the precast segmental arch members. As a result, it was found that the weaker longitudinal structural connectivity in the damaged culverts allowed the torsional displacements of the arch members to induce critical damage to the arch members, namely, edge defects in the arch crown and concrete foundation. The numerical results proved the unignorable influence of the longitudinal structural connection on the possible damage to three-hinged arch culverts.