Understanding the micromechanical events of interfacial failure in fibre reinforced composites is vital to accurately characterising micromechanical properties and, consequently, the macroscopic properties of the composite. A fracture mechanics model of the fibre push-out test is developed, with an emphasis on the effect of sample thickness and residual stresses on the mechanisms of interfacial crack advancement. The model is applied to both a SiC-SiC ceramic matrix composite and a SiC-Ti metal matrix composite. The model demonstrates that previous assumptions about the micromechanical events of interfacial cracking are consistent with the measured values of interfacial fracture energy for ceramic matrix composites. Moreover, the model can identify the range of geometries for which different micromechanical cracking mechanisms occur simultaneously in a given material system. Identifying this range is important in choosing the sample geometry for fibre push-out testing because the interaction of advancing cracks affects the measurement of interfacial fracture energy by classical models.