A stretch/bend method for the in situ measurement of the delamination toughness of coatings attached to substrates is described. A beam theory analysis is presented that illustrates the main features of the test. The analysis is general and allows for the presence of residual stress. It reveals that the test produces stable extension of delaminations, rendering it suitable for multiple measurements in a single test. It also provides scaling relations and enables estimates of the loads needed to extend delaminations. Finite element calculations reveal that the beam theory solutions are accurate for slender beams, but overestimate the energy release rate for stubbier configurations and short delaminations. The substantial influence of residual stress on the energy release rate and phase angle is highly dependent on parameters such as the thickness and modulus ratio for the two layers. Its effect must be included to obtain viable measurements of toughness. In a companion paper, the method has been applied to a columnar thermal barrier coating deposited onto a Ni-based super-alloy.