The boundary element method (BEM) is used to analyze the stress transfer behaviour in the single fibre push-out test. The result shows that the stress distributions are well compared to those obtained From the shear lag analysis for the majority of the embedded fibre length. The BEM analysis clearly depicts the singular behaviour of interface stresses, particularly the radial and shear stress component, at the loaded and supported fibre ends. The sheer lag analysis is unable to describe the stress singularity at these free edges. The implications of the biaxial interface stress components are discussed with respect to the interface debond criteria.