Elastic stress transfer in the fibre pull-out problem has been investigated quite extensively using various shear lag analyses. These analyses grossly underestimate the severity of the stress concentration at the fibre-matrix interface. In this study, by using the total complementary energy approach, it is found that a stress concentration zone exists at the interface near the fibre entry. Compared to shear lag analysis, the interfacial radial stress at the fibre entry is found to be much higher and the interfacial shear stress reaches a maximum not at the entry end of the fibre but in a few fibre diameters from it. It is also shown that the magnitudes of these stress peaks reduce with increasing b/a and L/a ratios. At large b/a and L/a ratios, the maximum radial and shear stresses at the interface reach a plateau and are independent of the loading methods considered. Finally, the implications of these stress concentrations on the failure of the matrix and interface and the specimen geometry in determining the interfacial shear strength are discussed.