Various crystalline nanostructures, such as silicon nanowires and nanotubes are promising in high-capacity lithium-ion batteries due to their excellent fracture resistance. Progress has been notably made in studying the mechanical behaviors in these structures. However, understanding the dynamic fracture under anisotropic swelling still poses some challenges. Here we have developed a concurrently coupled chemo-mechanical model considering two-phase diffusion, elastic–plastic deformation, and crack growth based on peridynamics to simulate the dynamic behaviors in the core–shell nanostructures with coexisting Li-rich and Li-poor phases. Our model includes several key features observed in the experiments, including sharp phase interfaces, anisotropic interfacial migration velocities, lithiation-induced large deformation, and fracture-pattern formation. The chemo-mechanical simulations predict that cracks are formed and propagate between two adjacent <110> orientations. In addition, our simulations also demonstrate that, compared with solid nanowires, nanotubes can facilitate lithium-ion diffusion and better resist failure. Understanding the mechanisms of different fracture patterns under anisotropic swelling in nanowires and nanotubes provides a basis for the design of new failure-resistant nanostructures in the future.