An analytical modelling approach is presented which is capable of determining the post-buckling responses as well as the onset of delamination growth of multi-layered composite plates with an embedded circular delamination. In order to overcome current drawbacks of analytical models regarding embedded delaminations, the model employs a problem description in cylindrical coordinates and a novel geometric representation of delamination growth in conjunction with a Rayleigh-Ritz formulation and the so-called crack-tip element analysis. The modelling approach is applied to study the compressive response of composite plates with thin-film delaminations loaded under radial compressive strain. Post-buckling responses and the onset of delamination growth are determined for several layups. The results are in very good agreement with finite element simulations while requiring low computational cost.