Robust and efficient predictions of buckling-driven delamination propagation, enabled by a novel analytical modelling approach, are presented. The model considers full mechanical coupling (extension-shear, extension-bend, extension-twist/shear-bend and bend-twist), contact and mode-mixity and thus significantly enhances the capabilities of current analytical approaches. A problem description in cylindrical coordinates enables the evaluation of the energy release rate along the delamination boundary. The model uses an energy formalism to determine the post-buckling deformation and a crack-tip element analysis employing force and moment resultants acting on the delamination boundary to determine the energy release rate. Composite panels with circular thin-film delaminations and various multi-directional stacking sequences are investigated for in-plane compressive loading. Predictions of applied strains causing delamination growth, i.e. threshold strain, show good agreement with published experimental data and 3D finite element analysis. A parametric study varying the ratio of delamination size to depth is performed. Based on the findings obtained, governing deformation characteristics of buckling-driven delamination growth are identified and insight into damage tolerant design of composite laminates is obtained, which is of particular interest for compression after impact (CAI) strength of composite structures.