The impact-induced buckling and delamination of a thin coating was analysed for the purpose of predicting the amount of coating removed when a single particle was launched, at a given velocity, against a coated substrate. A novel post-buckling analysis is presented in which the coating is modelled as a clamped disk prevented from buckling at an arbitrarily set inner radius, due to the presence of the indenting particle. A method for calculating the arrest strain energy release rate and mode mix of interfacial delamination cracks, based on the coupling of the presented buckling analysis with an existing strain energy release rate analysis [1] is then presented. A method to estimate the critical interfacial shear stress at crack initiation is also outlined. An accompanying paper [2] compares experimental results with the results of this analysis, and shows how the results can be used in the context of blast cleaning.