The pipe jacking method is gradually attracting increasing levels of attention and is becoming an important method for constructing underground engineering. However, jacking large-size concrete pipes in urban core areas subjected to complicated geological conditions is still a big problem preventing the employment of the pipe jacking method, and further studies related to pipe jacking are required. This paper presents a case study on the construction of three parallel large-size reinforced concrete circular pipes in the upper-soft and lower-hard composite formations, in which the construction work was implemented using the slurry balance pipe jacking method with the sequence of jacking the 1# and 3# pipes prior to the 2# pipe being implemented in field construction. This case study was implemented by employing numerical simulations with the aforementioned pipe jacking sequence, which focused on the stress and deformation variations of the reinforced concrete circular pipes, as well as the vertical settlement of the ground surface during the jacking processes, and considering the influences from the excavation pressure and grouting pressure of the drag-reducing thixotropic slurry. The simulation results revealed that a higher excavation pressure from the pipe jacking machine can easily induce an excessive pushing and squeezing effect of the excavated soil with the uplift phenomenon, while the increasing grouting pressure can be used to reduce the overall vertical settlement of the ground surface, whereas an excessive grouting pressure may have no effectiveness on protecting the reinforced concrete circular pipes. This work provides the numerical foundations for investigating the behavior of jacked parallel large-size reinforced concrete circular pipes.