In this study, a 3D finite element analysis (FEA) is performed to examine the seismic behaviors of a three-hinge modular underground arch bridge (MUAB) subjected to a series of synthetic ground motions with a wide peak-ground-acceleration (PGA) spectrum. The FEA model of the MUAB under longitudinal and transverse synthetic ground-motion loading is described by several modeling parameters [e.g., arch-to-arch interaction (AAI), soil–structure interaction (SSI), and stiffness of prestressed rebar], to determine its various seismic response characteristics (i.e., maximum displacement, maximum tensile and compressive stresses, and maximum crack depth). The FEA results show that the MUAB’s seismic responses differ with respect to earthquake-loading direction owing to the different levels of seismic resistance associated with the considered modeling parameters. To elucidate the influence of each modeling parameter on the seismic response, we performed MUAB parametric studies featuring different arch lengths, SSI and AAI friction coefficients, and prestressed-rebar stiffnesses. The key findings indicate that the seismic behaviors of MUABs depend on the PGAs and ground-motion directions; furthermore, they exhibited a sensitivity to the arch length and prestressed-rebar stiffness. In addition, the SSI friction coefficient exerted a minor influence on the seismic responses of MUABs, especially on their maximum compressive and tensile stresses and maximum crack depths; meanwhile, the AAI friction coefficient had a moderate influence upon seismic response.