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The research on the influence of radial stress on the mechanical properties of an anchorage structure has important theoretical and practical significance for optimizing the design of anchorage structures and saving support cost. Firstly, based on the phenomenon of concrete splitting found in the laboratory model test, the influence of radial stress on the mechanical properties of an anchorage structure is analyzed. Secondly, using the criterion of maximum tensile stress and the Mohr–Coulomb criterion, the influence of radial stress on the mechanical properties of rock around the borehole is analyzed. Finally, the influence of radial stress on the shear stress at interface and the ultimate bearing capacity of the anchorage structure is studied by numerical simulation. The results show that the existence of radial stress in the anchorage section greatly improves the bearing capacity of the anchorage structure. With the increase of confining pressure, the maximum value of interfacial shear stress increases obviously. The larger the confining pressure is, the faster the convergence speed of the finite element method (FEM) program is, which shows that the mechanical properties of the anchorage structure are improved obviously. With the increasing confining pressure, the adaptability of the anchorage structure to deformation is stronger and the anchorage structure is less likely to fail. The ultimate bearing capacity of the anchorage structure increases linearly with the increase of confining pressure, and the effect of confining pressure on the ultimate bearing capacity is very significant.