The RSS has been widely used in directional drilling. In order to enhance wellpath control accuracy and efficiency of the static push-the-bit RSS, a powerful BUR prediction method is reconstructed by coupling a rotary steerable bottom-hole assembly (RSBHA) mechanical model and a drill bit–rock interaction model. This article showed that when establishing the RSBHA mechanical model by using the continuous beam column method, the steering rib should be treated as an eccentric stabilizer to consider the contact effect between the steering rib and wellbore wall. For the beam column containing the flexible sub and between two stabilizers, it should be rearranged into three beam columns, and the lower and upper steps of the flexible sub should be considered as virtual supports. The equilibrium tendency method (ETM) to predict the BUR can enhance wellpath prediction accuracy than those of traditional methods. Under 3D conditions, the total drilling tendency angle should be denoted by inclination tendency angle and azimuth tendency angle to enhance the solution efficiency. Case analyses have verified that the average forecast error of the BUR prediction model in this article is less than 1°/30 m.