This investigation lies within the focus of aeroelastic analyses of uncertain structures in hypersonic flow conditions. Given the uncertainty, aleatoric or epistemic, on the structure, it is computationally advantageous to reduce the aerodynamic model complexity as long as the induced epistemic uncertainty is “small” enough not to affect the band of predictions of the response. Within this perspective of uncertainty management, it is desirable to have computationally very efficient, physically-based, surrogates of the fluid forces that provide approximate fluid forces with tunable accuracy. Moreover, such surrogates should be stochastic in that the aerodynamic epistemic uncertainty should be included and modeled. The present investigation provides some recent efforts toward the constructions of such stochastic surrogates in which the pressure is expressed as a sum of a local component, modeled with piston theory, and a global one.