Matrix softening is the decrease of stress with increasing strain in a plastic regime of deformation. This behaviour is normally followed by stress recovery. Matrix softening is disregarded in current models for strength and damage progression of fibre-reinforced composite materials that use finite element modelling [1]. This assumption eases the challenge associated with the instability of the finite element models when the materials soften. The linear-elastic perfect-plastic model disregards the onset of plastic flow and strain softening stages. Of course, the matrix response plays a key role in determining load sharing when a fibre breaks. Therefore, with a softening region in the matrix, we expect to see a faster evolution of the plastic-process zone surrounding the fibre break. We found that the evolution of the plastic region translates to faster-decaying stress concentration factors in the neighbouring fibres. To do this, we used finite element models to create a 50% fibre volume fraction hexagonal packing. Our model comprises epoxy Sicomin SR8500/KTA313 reinforced with HYBON2026 glass fibres. We represented the matrix in two ways: a linear-elastic perfect-plastic behaviour and an elastoplastic behaviour that included softening. We use two measurements to visualize the effect of the matrix softening, the stress concentration factor (SCF) and the local stress concentration factor (LSCF). The stress concentration factor is the volume-weighted cross-sectional stress average. The local stress concentration factor calculates the relationship between the maximum stress and the remote stress in each cross-section. Our results reveal that the softening behaviour of the matrix causes up to a 9% lower LSCF in neighbouring fibres while the SCF was lowered by up to 3%, see Figure 1. Nevertheless, comparing SCFs and LSCFs can help us bridge the gap between experimental and predictions of strength in composites. With this in mind, SCFs cannot express the same sensitivity to the localized stresses generated by a broken fibre. Therefore LSCFs offer insights complementary to SCFs.