A strength-based model for the single-fibre push-out test has been developed. Using this model, the matrix stress, fibre stress and interfacial shear stress in a single fibre specimen subjected to push-out loading was considered. The effect of physical and geometrical factors on the stress distribution were evaluated in terms of the influence of relative moduli and sizes of the matrix and fibre, respectively. The propensity for debonding crack initiation at the interface arising from matrix yielding (due to normal stress) and interfacial yielding (due to shear stress) has been determined. The influence of these on the location of debonding crack initiation and the maximum debond force has also been studied.