The paper presents results of very large amplitude squeeze-film damping simulations in Micro-Electro-Mechanical Systems (MEMS), using the different level models: 3D numerical solution of Navier-Stokes equations (using CFD-ACE+ from CFDRC), and circuit/behavioral models (in Spice and Saber-MAST formats). The results of the compact model, based on nonlinear RL equivalent circuit, agree very well with the 3D results even for very large amplitudes of plate motion, accompanied by significant changes of pressure. For the amplitudes reaching 90% of the nominal gap distance between plates, the relative pressure change due to squeeze forces is 10 to 15 times bigger than the static ambient pressure force. All previous squeeze film simulations published by other authors were limited to small amplitudes and small pressure changes only. The Saber version of the model has been implemented in the hierarchical MEMS-CAD system NODAS (Nodal Design of Actuators and Sensors) from Carnegie Mellon University. Examples of NODAS simulations, with the use of the behavioral squeeze film damping model, are also presented.