Abstract: The curvature-forming mechanism and directional control present fundamental theoretical challenges impeding the advancement of curved rectangular pipe jacking technology. This study proposes an active curvature-forming method that integrates an articulated multi-unit rectangular tunneling machine with coordinated cutterhead over-excavation. A mechanical model describing the interaction between the machine’s front and rear shields and the surrounding stratum during curved advancement is established, enabling dynamic and precise calculation of the deflection angle, stratum reaction force, and the required thrust of the directional control jacks. Through numerical case analyses, the influence mechanisms of key parameters, including curve radius, overburden depth, soil internal friction angle, stratum reaction coefficient, and force arm length on thrust distribution are systematically investigated, validating the model’s rationality and applicability. The results demonstrate that increasing the soil internal friction angle or reducing overburden depth significantly decreases the peak thrust, whereas increasing the stratum reaction coefficient or decreasing the curve radius substantially elevates the thrust acting on the outer jack. When the curve radius reduces below a critical threshold, the inner jack thrust transitions from positive to negative, causing the machine to shift from a “dual-side thrusting” mode to an “outer-pushing, inner-pulling” operational pattern. This research provides a theoretical foundation for precise construction control and equipment optimization in curved rectangular pipe jacking applications.