Aerodynamic support is beneficial for achieving very high speeds of marine transportation. Wing-in-ground vehicles, power-augmented ram platforms, and ultrafast planing multihulls are examples of marine craft with air assistance. The main technical problems in the development and application of these concepts for marine transportation are to ensure motion stability and to provide adequate seaworthiness. In this article, we illustrate applications of several mathematical models for various air supported marine vehicle concepts and discuss their specific stability issues. The aerodynamic submodels are based on nonlinear vortex–lattice methods and on the extreme ground effect theory, whereas unsteady hydrodynamics of planing surfaces are treated with added-mass strip theories. The static and dynamic stability in the vicinity of equilibrium states can be analyzed by linearized approaches. However, motions in transient regimes and unsteady environments require implementation of nonlinear and fully unsteady modeling methods.