The entrainment phenomenon in two-phase parallel flow has been studied from the standpoint of wave instability theories, which are related to the exponential growth of unstable waves caused by viscous interaction between the two parallel flowing fluids. Instability theories related to the Kelvin-Helmholtz and the Orr-Sommerfeld problems were reviewed and applied to predict the critical air/vapor velocity at the onset of entrainment from a capillary structure. To compare the theoretical criteria with the experimental results, entrainment observed in both air-water and steam-water situations were characterized and classified into three major categories. As results of these comparisons, a modified theoretical criterion based on the results of Miles was developed and used to investigate the effect of liquid depth on the critical air/vapor velocity or corresponding Weber number for the given temperatures, and general trends of the various criteria were examined as a function of vapor temperature.