An aluminium (Al, 2024T3) matrix composite reinforced with continuous alumina (Al2O3) fibres is investigated under tensile off-axis constant macro stress and thermal cyclic loading. The micromechanical approach to modelling and three different fibre cross-section geometries have been employed. The effect of creep is included by considering three dwell times at the peak temperature of the thermal loading history. The presence of the hold time gives rise to different sources of failure such as cyclic enhanced creep and creep ratchetting. These failure mechanisms are carefully discussed and assessed. The linear matching method framework has been used for the direct evaluation of the crucial parameters for creep-fatigue crack initiation assessment at the steady cycle. A detailed representation of the steady-state hysteresis loops is provided by using the strain range partitioning and a method for dealing with multiaxiality is reported with regard to the algebraic sign of the Mises-Hencky equivalent stress and strain. All the results obtained have been benchmarked by fully inelastic step-by-step (SBS) analyses. The design of a long fibre metal matrix composite should consider not only the detrimental effect of their dissimilar coefficient of thermal expansion, but also the state of stress at the interface between the matrix and fibre.