Due to the shape discrepancy between the rectangular machine shell and the circular cutterhead, rectangular pipe jacking machines inevitably have cutting blind zones, which could waste thrust force and reduce tunneling efficiency. Few studies have been done in the past on the effects of the cutting blind zones on the jacking behavior of the rectangular tunneling machine. To investigate the performance of the rectangular pipe jacking machine under the influence of excavation blind zones, three-dimensional discrete element modeling was performed in this study, where various blind zone ratios (i.e. the area ratio of excavation blind zones to the rectangular excavation face) ranging from 2% to 10% were considered. The resultant velocity distributions of soil particles indicate that the soil stagnation phenomenon in the cutting blind zone near the non-overlapping zones between adjacent cutterheads can be alleviated by the staggered front-to-back arrangement of multiple cutterheads, while the stagnation phenomenon in the cutting blind zone close to the pipe shell is remarkable. Besides, it was advisable to keep the cutting blind zone ratio at about 5% in practical construction in view of the extra costs of over-arranging multiple cutterheads for a small cutting blind zone ratio as well as the waste of thrust force caused by an excessively large cutting blind zone ratio. Additionally, structural optimization strategies were proposed, which were intended to provide some guidance for the future design and improvement of rectangular pipe jacking machines.