<p>Soft robotic grippers equipped with pneumatic airbags offer a promising solution for dynamic target capture by enabling compliant impact buffering and energy dissipation. However, the coupled mechanisms involving large geometric deformation, quasi-incompressible membrane behavior, internal gas dynamics, and nonlinear contact interactions remain insufficiently understood. This study proposes a multiphysics modeling framework for a pneumatic flexible airbag cushioning system considering compliant contact. The thin-walled airbag structure is discretized using triangular Absolute Nodal Coordinate Formulation (ANCF) membrane elements integrated with a stiffness reduction model to capture large deformation and wrinkling behavior. Internal gas dynamics are described using a control volume approach based on mass and energy conservation principles, while nonlinear normal contact forces are modeled using an improved Hertzian-based compliant contact formulation combined with a GGEOM contact detection algorithm. Impact experiments were conducted to validate the proposed model. The simulated contact force and kinetic energy evolution showed strong agreement with experimental measurements, achieving coefficients of determination of 0.927 and 0.971, respectively. Parametric analyses revealed that pressure relief and the exhaust rate act as dominant regulatory factors governing equivalent stiffness modulation, peak contact force suppression, rebound mitigation, and kinetic energy dissipation efficiency. Specifically, increasing the exhaust rate reduced the peak contact stress by up to 23.4% and enhanced energy dissipation efficiency to 98%. The proposed model provides a physically interpretable and quantitatively validated framework for the design and optimization of pneumatic cushioning systems in dynamic grasping applications.</p>