An axisymmetrical finite-element model has been used to study the effect of matrix properties (elastic modulus, yield and/or cold draw strengths and yield strain) on the interfacial shear stress in a short embedded fibre and, consequently, the value of interfacial shear strength obtained from the fragmentation test. It is observed that the maximum shear stress at the fibre-matrix interface is related to matrix yield strength. The maximum shear stress at the interface is limited only to a very small portion of the fibre which is not the fibre end. However, at higher applied strains, a major portion of the fibre is subjected to a slightly lower value of interfacial shear stress, defined as `plateau shear stress', which corresponds to the cold draw strength of the matrix. Matrix yield strain is observed to be the major parameter controlling the fibre fragmentation process and the number of fibre fragments at saturation. It has been shown that the use of the elastic theories, such as the shear lag and finite difference models, for the normalization of the value of interfacial shear strength obtained from the fragmentation test is not appropriate since the data reduction technique for the fragmentation test assumes a perfectly plastic matrix. The value of the plateau shear stress is compared with the fragmentation test results and it is observed that the interfacial shear strength calculated from the fragmentation test can exceed the plateau value of the interfacial shear stress in certain cases. This discrepancy can be explained on the basis of limitations of the constant shear model. Further, the stress field developed around a short fibre embedded in a matrix is compared with existing one-dimensional and bi-dimensional models. It has been observed that one of the serious limitations of the various micromechanical models is to predict the area of influence caused by the presence of the fibre. Finite-element analysis is used to study the area of influence.