The aim of the paper is to check the accuracy of global plate models in predicting progressive damage and failure load of cross-ply laminated composite plates. The damage evolution model is based on a generalized macroscopic continuum theory within the framework of irreversible thermodynamics. The progressive damage analysis is carried out using global higher order shear deformation theory with/without thickness stretch and zig–zag terms, and first order shear deformation theory with shear correction factor of 5/6 and the one calculated accounting for layers’ properties and lamination scheme. For comparison, progressive damage modeling employing 3-D finite element is also done. The parametric study is carried out to assess the accuracy of higher-order model based on continuum damage mechanics for different span-to-thickness ratio, lamination scheme and boundary conditions. It is concluded that higher-order model with zig–zag terms in in-plane displacement and thickness stretch terms in transverse displacement predicts failure load and stress distributions quite accurately. The higher order model is computationally efficient since the number of unknowns is independent of number of layers. For two-layered thick laminates, first order model with shear correction factor calculated based on lamination scheme predicts significantly better results compared to that with shear correction factor of 5/6.