The effects of material properties and specimen geometric factors on stress transfer across the fibre-matrix interface in the fibre push-out test are evaluated based on an axisymmetric boundary element analysis. It is shown that the Young's modulus ratio of fibre to matrix, the effective fibre volume fraction, the specimen thickness and the support hole size influence significantly the overall interface stress profiles and the maximum stress values at free edges. The first two material in particular, dictate where the maximum interface shear stress occurs between the loaded and supported fibre ends. The implication is that under certain circumstances the interface debond may initiate from the supported fibre end, as opposed to the usual loaded end debonding, if assuming the maximum interface shear stress criterion. A similar two-way debond phenomenon is predicted using a shear lag analysis.