Abstract: To improve the borehole trajectory control effect and operation safety of rotary steerable tools, the analysis of the lateral vibration characteristics of rotary steerable bottom hole assembly (RSBHA) was conducted. A static push-the-bit rotary steerable tool can control borehole trajectories through its driving force produced from its three pads, and thus it can be regarded as an eccentric stabilizer with known eccentricity and eccentric azimuth. In this work, a three-dimensional statics model of RSBHA with small deflection was constructed to determine the spatial configuration of RSBHA under the weight on bit and the constraints of borehole wall by the weighted residual method, and thus to obtain the upper tangential point. Then, a finite element model was built, taking the distance between the upper tangential point and the bit as the effective length for lateral vibration. The lateral vibration responses of RSBHA could be elicited using the mode superposition method, and analysis of the influence of working and structural parameters on its lateral vibration could be made. The calculation results showed that when the rotary speed was around 138 r/min, the dynamic displacement of RSBHA was greater in the distances of 8.20 m, 18.10 m, 24.60 m, and 31.60 m away from the bit. The weight on bit had little impact on the maximum bending stress of RSBHA, while the eccentricity and eccentric azimuth had a greater impact on the lateral vibration characteristics, and the maximum bending stress would obviously increase for certain eccentricity and eccentric azimuth. The research shows that working and structural parameters have great influence on the lateral vibration of RSBHA, which should be optimized to ensure the proper application and operation safety of rotary steerable tools.