The long-term stability of stone cultural relics is a key concern in their preservation. This study focuses on the Bodhisattva statue in front of the reclining Buddha carved on Dazu Rock Carvings. Using bilateral filtering algorithm, the point cloud data from a 3D laser scanner were processed in the PCL platform to remove noise, preserving the surface details of the cultural relics. A refined 3D model of the Bodhisattva statue, including its fissure structure, was established. The statue’s stability was analyzed using the strength reduction method with FLAC3D software. The findings include: 1) The denoising method resultes in an average deviation of -5.0 mm to 4.0 mm and a standard value of 1.1 mm, which completely retained the artifact’s surface characteristics. 2) Under gravity load, the statue’s neck compressed while the top stretched, with cracks in the head redistributing internal stress, and the peak tensile stress moving from the top to the crack end. 3) The statue’s head displacement correlates positively with the reduction coefficient, sharply increasing at 1.28, indicating a tendency to tip. 4) The failure surface extends along the crack and neck into the relic’s interior, with the plastic zone and maximum shear strain increment forming a parabola through the two regions. This method offers insights for analyzing the stability of small stone artifacts with complex geometries.