The presented contribution focuses on the impact of the precipitation state in an Al(6061matrix phase on the crack initiation mechanisms in the Al(6061/Al2O3 composite under cyclic and monotonic loading. Through defined heat treatment it is possible to achieve different precipitate distributions, which in turn make the matrix "soft" or "hard". Presented results concentrate on the composite with the "hard" matrix. The observations of the crack initiation and crack growth on the polished specimen surface were performed using an optical microscope during low cycle fatigue tests. Short cracks occurred predominantly in the matrix phase. The first cracks appeared before the specimen reached a half of its lifetime and grew in the direction of the max. shear stress, inclined of about 45° to the loading axis. Subsequent microtomography analysis done on the undeformed and cyclically deformed specimens enabled the spatial reconstruction of the microstructure and in the damaged specimens the location and extension of the fatigue cracks. Tomogram based 3D-FE simulations of the cyclic loading have been performed using experimental parameters as boundary conditions. Both, experiment and simulations were conducted strain-controlled with an amplitude of 0.5% at R=-1. The mechanical behaviour of the matrix phase was simulated using a plastic material model of the Chaboche type.