The article reveals one of the main problems hindering the mass production of dynamic hovercraft – the problem of longitudinal instability, which can lead to a ship's turn; the criteria for stability of dynamic hovercraft are considered. We also studied ways to ensure the necessary stability. It is noted that the problem of ensuring the stability of vessels on a dynamic air cushion can be solved by creating an automatic stabilization system, or by choosing a special geometry of the bearing surfaces and their arrangement in the aerodynamic scheme – self-stabilization. An extreme problem of optimization of the bearing surface of a vessel on a dynamic air cushion located in a steady flow of an ideal incompressible fluid is considered.it is formulated taking into account the requirement of self-stabilization.