A significant challenge for wheel- and propeller-driven amphibious vehicles during swimming operations involves the egress from bodies of water. The vehicle needs to be able to swim to the ramp of a vessel, and then propel itself up the ramp using water propellers and wheels simultaneously. To accurately predict the ability of the vehicle to climb the ramp, it is important to accurately model: (1) the interaction of the flow through the propellers, around the vehicle hull, and away from the ramp; (2) the wheel / ramp interaction; (3) the suspension system spring, damping, and motion-limiting forces, tire deformation and loading characteristics, and wheel and hull motions (both translation and rotation); and (4) the drivetrain power distribution to the wheels. Detailed modeling and simulation of these physics and processes -- such as the wheel, hull, and suspension system motions and force interactions, propeller rotation and resulting flow, etc. -- would be highly computationally expensive. Therefore, to make the water egress problem more tractable to solve, various modeling simplifications -- such as the use of an actuator disc methodology for propeller flow modeling and Wong's terramechanics methodology for the wheel / ramp interaction -- were introduced to facilitate rapid simulation. The integration of a customized six-degree-of-freedom (6DOF) body dynamics solver with a multiphase Volume of Fluid (VOF) computational fluid dynamics (CFD) solver (STAR-CCM+) resulted in an efficient, robust, comprehensive methodology for modeling and simulating amphibious vehicle water egress for various environmental and vehicle characteristics and operational conditions.