Hydro-aerodynamic mathematical model and multi-objective optimization of a popular wing-in-ground effect craft are presented in this research using a hydro-aerodynamic practical method and the genetic algorithm. The primary components of the wing-in-ground effect craft configuration include a compound wing, catamaran hull form and a power-augmented ram platform. The hydro-aerodynamic practical method with low computational time and high accuracy is performed by coupling hydrodynamic and aerodynamic considerations using the potential flow theory in ground effect and the semi-empirical equations proposed for high-speed marine vehicles. The trade-off between hydrodynamic and aerodynamic characteristics makes it difficult to simultaneously satisfy the design requirements of high hydro-aerodynamic performance. In this article, three goals—reduced hump resistance, increased compound wing lift-to-drag ratio and reduced take-off speed—are selected as the objective functions. The longitudinal position of center of gravity, position of outer wing with respect to main wing, power augmented ram platform angle to horizontal and flap angle are also adopted as design variables. Static height stability and the location of the center of gravity with respect to the aerodynamics centers are considered as constraints for the stable flight in ground effect. The optimal solutions of the multi-objective optimization were not unique, rather a set of non-dominated optima, called the Pareto sets, are obtained. As a result of the multi-objective optimization, 25 Pareto individuals are obtained that the naval architects can use in designing wing-in-ground crafts. © IMechE 2017