In a three-line parallel shield tunnel, the construction of a second shield tunnel may affect existing advanced tunnels. An analytical solution for the additional horizontal displacement of the leading tunnel after two parallel side passes of the shield was obtained by establishing a two-stage analysis model and using the Mindlin solution. The effectiveness of the method was verified using measurement data from the Shanghai X-ray shield tunnel. A parametric analysis was performed to investigate the effects of the horizontal distance between the tunnels, longitudinal stiffness of the tunnel structure, shear modulus of formation, and ground loss on the tunnel responses. The results showed that the additional displacement peak generated by the first tunnel under the parallel side crossing of the second tunnel was inversely proportional to the horizontal distance of the parallel tunnel, longitudinal stiffness of the tunnel structure, shear modulus of the formation, and formation loss rate in direct proportion. The proposed method can provide a theoretical basis for predicting the influences of two parallel side passes of a shield on an existing advanced tunnel in relevant engineering practice.