This paper investigates theoretically the compressive load-carrying behaviour of geometrically imperfect web-core sandwich plates. Slender plates, which first buckle globally, are considered. The study is carried out using two approaches, both solved with the finite element method. The first is the equivalent single-layer theory approach. First-order shear deformation theory is used. The second approach is a three-dimensional shell model of a sandwich plate. Plates are loaded in the web plate direction. Simply supported and clamped boundary conditions are considered with a different level of in-plane restraint on the unloaded edge. The results show that the behaviour of the sandwich plate is qualitatively equal to the isotropic plate of the same bending stiffness for deflections lower than the plate thickness. As the deflections increase, the lower in-plane stiffness of the sandwich plate results in lower post-buckling stiffness. Local buckling of face plates in the post-buckling range of the sandwich plate further reduces the structural stiffness.