The problem of face wrinkling in sandwich structures was identified as an important failure mode and first analyzed in 1940 by Gough et al. [1], who used a Winkler-type elastic foundation to model the core. This work was followed by experiments and further analysis by many others. Until 1966 all of the research was devoted to uniaxial compression loading. However, in many applications, such as naval and aircraft structures, panels are subjected to biaxial loading. Such loadings were first analyzed by Plantema in 1966 [2] for the case of sandwich constructed of isotropic materials. Sullins et al. [3] suggested an interaction equation that can be used as a criterion of wrinkling under compression in the principal directions. This equation is formulated in terms of the ratios of the principal compressive stresses to the corresponding wrinkling stresses. More recently Fagerberg [4, 5] and Vonach and Rammerstorfer [6] considered the case of sandwich with orthotropic facings. The present work attacks the subject problem using three different models for the core. One model uses a simple Winkler elastic foundation approach. The second model, following Hoff and Mautner [Hoff, N.J. And Mautner, S.E. (1945). The Buckling of Sandwich-Type Panels, Journal of the Aeronautical Sciences, 12: 285-297.], uses a linear model for the decay in deformation from the core-facing interface, while the third model, following Plantema [Plantema, F.J. (1966). Sandwich Construction, John Wiley & Sons, Inc., New York.], uses an exponential decay.