This study investigates the influence of subsequent tunnel boring machine (TBM)-driven processes on the responses of the first tunnel in twin-tunnel construction using the ultra-rapid underground pass (URUP) method. A comprehensive finite element analysis (FEA) is performed to simulate the URUP TBM tunneling, considering the non-uniform convergence caused by the TBM geometry, the tunnel face supporting pressure, and the tail-grouting pressure. The FEA model is validated by the monitoring results of the bending element of the first tunnel lining. The FEA results reveal that the grouting pressure of the second tunnel has significant influence on lining deformation of the first tunnel, while the face supporting pressure shows little effect. The relationship between the grouting pressure and the maximum bending moment of adjacent first tunnel can be fitted by linear function. A grouting pressure equals to the lateral earth pressure is able the reduce the variation of the bending element of the first tunnel during the TBM-driven process of the second tunnel. The bending element of the first tunnel shows a typical lognormal relationship with the face supporting pressure during the TBM advance of the second tunnel. A critical cover-to-depth ratio, under which the horizontal and vertical soil arching effect vanishes, can be deduced to be within the range of 0.55–0.60.