The load transfer characteristics of a tensile anchor in the rock mass with weak interlayers are investigated, considering the non-uniform stress of the surrounding rock along the bolts. A improved shear-slipping model is proposed to describe the stress evolution characteristics of the bolt-rock interface. Based on the proposed improved model, analytic solutions of axial force, shear stress distribution and load-displacement relationship considering the residual stress stage are established. The effects of the stratigraphic sequence, pulling force and bolt diameter on the stress distribution of the anchorage interface are evaluated using analytical solutions, and the results are verified using the finite difference numerical simulation method. Finally, in light of the calculation of the sensitivity coefficient, the sensitivity of each parameter to the axial force and shear stress of the rock bolt are determined. Study results show that the tend of the axial force and shear stress to decrease unevenly along the rock bolt towards the anchorage depth. Due to the existence of weak interlayers, the stress characteristics of the rock bolt in the weak interlayer are significantly different from those in the hard rock. The shear stress is mutated at the weak and hard rock interface, and the axial force appears to “rebound” at the bottom of the anchored section. The pulling force and stratigraphic sequence directly affect the distribution of shear stress at the anchorage interface. This study completes the theoretical framework for the fundamental problem of tensile bolts in horizontally or vertically laminated rock masses, providing a theoretical basis for anchor design.