The paper is an application of the author's general theory of sandwich plate (Ref. 1). Since the deformation is very small when buckling starts, the problem can be considered as a linear case. The theoretical critical stress found by this theory shows different types of buckling; symmetric and anti-symmetric, qausi-eulerian and wrinkling. The minimum symmetrical buckling stress found by the present theory, unlike most previous theoretical results (with isotropic core), is not always greater than the anti-symmetric buckling stress. In comparison with the existing theories, the theoretical results of the present work show better agreement with experiments for all types of buckling. The critical wrinkling stresses decrease when, other things remaining the same, the core to face thickness ratio decreases. This is verified by many wrinkling failures in the Forest Product Laboratory tests (Ref. 10, 11, 12). Previous theories with isotropic core theory have so far failed to indicate this fact. Comparison of the compression buckling of rectangular plates with two (the two loaded edges simply-supported, the other two being free) and four simply-supported edges has also been given in order to show the effect of the two additional supports.