In this study，a three-dimensional finite element analysis method was used to simulate tunnel excavation nearby a perpendicularly crossing existing tunnel，in order to investigate the effects of construction sequences on cross-cutting tunnels. The hypoplastic constitutive model of sand and soil is adopted and the soil small-strain stiffness is considered in the numerical analysis，so as to study the effect of construction sequences on cross-cutting tunnels as well as the stress transfer mechanism of the soil near the existing tunnel. The results show that the existence of the existing tunnel reduces the maximum settlement by 14% when compared with the condition without the existing tunnel; when the new tunnel is above the existing tunnel，the settlement is larger，but the impact range is smaller. When the tunnel face approaches the centerline of the existing tunnel，the stress of the existing tunnel is transferred from the vault to the abutment；when the tunnel face is between 3D behind and 6D in front of the centerline of the existing tunnel，the effect of stress relief on the existing tunnel is significant; when the new tunnel is under the existing tunnel，the deformation and bending moment of the existing tunnel are greater. In the construction of vertical cross tunnels，the impact of the construction sequence on the ground settlement and the existing tunnel should be considered comprehensively.