Flexible drill rods, which are prized for their excellent bending performance, are extensively employed in the redevelopment of mature oilfields via ultra-short radius horizontal wells. However, the lack of accurate mechanical analysis of their dynamic drilling process has often resulted in imprecise predictions of rod deformation and load transfer. In this study, a nonlinear finite element model and a numerical solution method were established for the flexible drill rod and the wellbore wall, with consideration given to the dynamic drilling process and the articulated multi-segment characteristics, to simulate the drilling transition from the vertical section into the build-up section. It was revealed that the drill rod undergoes significant bending deflection during operation. The axial force at the upper end was found to exhibit a distinctive three-stage variation pattern-characterized by rapid increase, steady gradual growth, and fluctuating slow increase-while the distribution of contact force against the wellbore wall showed no obvious regularity, and the rod velocity was observed to fluctuate markedly at the initial stage and at the junction between the vertical and build-up sections. Furthermore, parametric analysis indicated that a flexible drill rod with a single-segment length of 200 mm and a limit rotation angle of 5° experiences the least frictional resistance during the build-up section, thereby yielding the highest load-transfer efficiency and the best overall drilling performance. The findings of this study are expected to offer a valuable reference for the structural optimization of flexible drill rods.