This paper deals with the buckling problem of antisymmetric angle-ply laminated circular cylindrical panels subjected to a uniform axial compression. Since a flat plate configuration occurs as a particular case of the cylindrical panel geometry (zero shallow angle parameter), the corresponding flat plate problem is studied as a particular case of the problem considered. The theoretical analysis is based on a nonlinear theory developed in a previous paper (Soldatos, 1992), which accounts for parabolically distributed transverse shear strains through the shell thickness. The linearized differential equations, governing the buckling behavior of a simply supported panel, are solved on the basis of Galerkin's method. Comparisons of corresponding numerical results based on both the refined shell theory employed and a classical Love-type shell theory, show the influence of transverse shear deformation on the buckling loads of such laminated composite panels.