Seismic calculation of double-arch tunnels subjected to near-fault ground motions faces the challenge of simultaneously accounting for the double-arch geometric effect at the tunnel crown, the near-fault velocity pulse effect, and the significant vertical seismic effect. To address this issue, a theoretical calculation method specifically designed for the transverse seismic analysis of double-arch tunnels in near-fault regions is established. First, the limitations of the conventional response displacement method, which directly equates the tunnel boundary displacement to free-field displacement, make it difficult to capture the interactions among the middle wall, overlying soil, and tunnel structure. To overcome this, a generalized structural seismic mechanical model is developed that incorporates the double-arch tunnel structure and a range of surrounding rock. This model defines free-field relative displacement, boundary shear stress, foundation spring constraints, and structural seismic inertial forces, leading to a comprehensive calculation procedure. Next, based on dynamic time-history numerical simulations using near-fault pulse-like ground motions, the relationships among the peak accelerations of the main tunnel, middle wall, and ground-motion intensity parameters are analyzed. From this analysis, calculation formulas for structural seismic inertial forces are established by considering both horizontal and vertical peak ground accelerations along with burial-depth corrections. Based on a comparison of the differences between theoretical calculations and numerical results across various boundary ranges, a method for determining the reasonable transverse and vertical extents of the generalized structural region is proposed. The validity of the proposed theoretical method is confirmed through a combination of numerical simulations and vibration platform tests. Finally, parametric analyses are conducted to explore the effects of structural geometry, burial depth, and ground-motion parameters on structural seismic responses. The results show that a moderate increase in the width-to-height ratio of the middle wall can reduce stress concentration, whereas a ratio exceeding 0.20 may significantly increase lining stress. An increase in burial depth tends to favorably shift the structure toward a compression-dominated stress state. In addition, enhancing near-fault vertical ground motion, with the PGA_v/PGA_h ratio increasing from 0.7 to 2.0, can amplify stresses at critical locations by 16.7% to 130.5%. The velocity pulse effect, represented by the PGV/PGA ratio, significantly influences the outer side of the lining and the middle wall, with stress levels sharply increasing in the interval of 0.15 to 0.27 s.