Concentric tube robots (CTR) have garnered significant attention in minimally invasive surgery due to their high flexibility. However, their clinical application has been severely restricted by “snapping” caused by an elevated bending-to-torsional stiffness ratio (EI/GJ), which risks tissue damage. To address this challenge, this study proposes an iso-geometric analysis (IGA)-based topology optimization framework aimed at enhancing structural stability through the reduction of the EI/GJ. By establishing a parametric physical model using NURBS and plate and shell theory, combined with anisotropic material design, the iterative optimization of tubular topology configurations was achieved. The optimization process aimed to minimize EI/GJ under a volume fraction constraint of 0.6. Numerical experiments demonstrate that concave diamond-shaped structural patterns significantly reduce the EI/GJ, achieving improved stability compared to traditional patterned structures. Finite element analysis (FEA) verification confirms that the optimized design effectively suppresses snapping while maintaining excellent bending flexibility. This research provides a novel methodology for optimizing the high-stability topology of minimally invasive surgical instruments, which could improve the workspace and multifunctional trajectory capabilities of concentric tube manipulators.