Abstract: Objective Accurate build-up rate prediction of rotary steerable tools is a prerequisite to achieve the precise control of tools. In order to grasp the variation law of the build-up rate of the rotary steerable bottom-hole assembly (RSBHA). Methods Based on the structural charaeteristics of the tool, the Euler-Bernoulli beam equation method is used to analyz the forces outing on the composite RSBHA. At the same time, the calculation method of the tool deflection angle in different sections and the bit pre-drilling deflection angle was obtained with consideration to the geometric relationship of the bottom-hole assembly, and the distance between the connecting points of rotary steerable tool and bit was taken as the spatial delay period. Finally, a prediction model for the build-up rate of the RSBHA based on delay differentiation was established. This model comprehensively considers the qualitative influence of parameters, such as the geometric size and structure of the tool itself, the cutting anisotropy of the drill bit related to the formation, the weight on bit, and the bending stiffness related to the tool material and the inner and outer diameters, on the build-up rate. Results and Conclusions The study shows that: (1) The predicted results of this model are in good agreement with the simulation results of Schlumberger's mature build-up rate prediction software based on the finite element analysis, and the difference between the predicted results is maintained within 0.5 (°)/30 m, which meets the engineering requirements. (2) This method can also compensate for the measurement error caused by the distance between the drill bit and the measurement unit based on the actual measurement data of the drilling tool attitude gauging nipple, providing a new way to solve the problem of unmeasurable are. This build-up rate prediction method based on spatial delay differentiation provides theoretical basis and rapid analysis means to optimize the structure of RSBHA and the drilling parameters. The established model is easy to simulate and transplant, and can obtain good real-time response in practical engineering applications, which provides an accurate foundation of drilling tool movement model for the development of rotary steerable tools based on digital twins.