A superhydrophobic coating can be produced using a hydrophobic material textured with surface roughness on the micro-/nano-scale. Such a coating on the outside of a submersible body may result in reduced skin-friction drag due to a trapped layer of air in the coating. However, this layer may become unstable when subjected to elevated hydrostatic pressures, and a coating’s performance is compromised beyond a certain threshold (critical pressure). This thesis presents a numerical model for predicting the pressure tolerances of superhydrophobic coatings comprised of randomly deposited hydrophobic particles or fibers. We have also derived a set of force-balance-based analytical equations for predicting critical pressure in surfaces with ordered roughness, and compared our numerical model against it, observing reasonable agreement. The numerical model was then applied in a large parameter study, predicting critical pressure for coatings with a given set of microstructure properties.