Aligned-discontinuous-fibre reinforced polymers have the potential to combine (i) the high specific stiffness and strength and light weight of conventional continuous-fibre composites with (ii) increased damage tolerance, improved manufacturability, and the ability to close the life-cycle loop of composites by using recycled fibres. However, predicting the mechanical response of discontinuous composites is a challenge for which no universally accepted and computationally-efficient solution exists yet. This paper presents a model for aligned discontinuous-fibre reinforced composites considering (i) a generic constitutive law for the matrix, (ii) stochastic fibre failure under non-uniform stress fields due to the presence of fibre-ends, and (iii) unstable final failure from a critical cluster of damage. Results show good agreement with experiments from the literature, and the model also stresses the importance of considering the stochastic nature of both the fibre-end locations and the fibre-strengths to model aligned discontinuous composites. Parametric studies suggest that failure of aligned discontinuous composites depends on (i) the overlap length between fibres for short-fibre composites, and (ii) the fibre strength for long-fibre composites; intermediate-length fibres would result in discontinuous composites with maximum stiffness, strength, and failure strain simultaneously.