The postbuckling behavior of composite flat panels subjected to uniaxial/biaxial compressive loads is investigated. To this end a refined geometrically nonlinear theory of composite plates is developed. The effects played by transverse shear deformation, initial geometric imperfections, the character of the in-plane boundary conditions and lamination are studied and a series of pertinent conclusions are outlined. Throughout the paper, the results obtained within the transverse shear deformable plate model are compared with their classical counterparts and conclusions related to their range of applicability are presented.