Abstract: To address the safe grasping requirements for thin-walled deformable containers, a mechanical finger composed of an alloy steel skeleton and a silicone rubber inner liner was constructed. Three-dimensional nonlinear contact simulations were carried out with a paper cup and an ABS cup as the target objects, respectively. A displacement-controlled method was adopted to simulate two clamping displacements of 0.5 mm and 1.0 mm, totaling four working conditions, and the stress, strain and displacement response data were collected. The study reveals the nonlinear stress attenuation law of the flexible inner liner along its thickness direction, and compares the plastic extension of the cup body and the differences in contact uniformity under different conditions. These results can provide a numerical basis and criterion for the parameter optimization of the gripping interface of the mechanical finger.