A three-dimensional unit cell has been developed and modelled using the finite element method to investigate the interface failure behaviour of SiCf/Si3N4 composites under tensile loading at room and elevated temperatures. The model idealizes the composite as a regular rectangular array of fibres in 0 degrees and 90 degrees orientations embedded in the matrix. It introduces three-dimensional contact elements between the fibre and the matrix to simulate the interface conditions between the two phases. Slippage between 0 degrees and 90 degrees layers is also considered by introducing another set of contact elements at the layer separation planes. Two interface conditions, namely, infinitely strong and weakly bonded, are considered to establish the correlation with the experimental data. To simulate the weak interface, the fibre and the matrix are assumed to slide over one another with shear stress through the Coulomb mechanism. The same assumption has been adopted for the layer separation planes. A finite element model utilizing these concepts has been developed. Stress-strain behaviour and the local stress distributions at various ambient temperatures within the unit cell, are presented. The investigation has also been extended to include the effects of residual stresses in the finite element model. It is shown that the model yields results th at correlated reasonably well with the experimental data.