Ceramic matrix composites reinforced by unidirectional long ceramic fibre are very perspective materials. The only disadvantage of such materials is relatively high brittleness at room temperature. The main micromechanism acting as toughening mechanism is the pull out. There are other mechanisms as crack bridging, crack deflection etc. but the primer mechanism is mentioned pull out which is governed by interface between fibre and matrix. The contribution shows a way how to predict and/or optimise behaviour of composite by application of cohesive zone method using the FEM numerical package Abaqus. The presented results from numerical calculations are compared with experimental data.