Fibre break models are powerful tools to study the tensile strength of unidirectional (UD) composites, and how they are affected by the fibre and matrix properties. So far, however, most models have been limited to studying the static tensile strength [1]. Some models have been extended to account for cyclic loading [2,3], which further increases their usefulness. Extensions of advanced fibre break models towards time-dependent properties, such as creep and stress relaxation, however, remain scarce. The most significant development in this regard is the model of Blassiau et al. [4]. Unfortunately, their model was not based on actual measurements of the viscoplastic properties of the matrix. This paper therefore describes the extension of the KU Leuven fibre break model [1] towards time-dependent properties based on measured viscoplastic behaviour of the matrix. Our study focuses on the combination of carbon fibres with an epoxy matrix. The epoxy matrix was tested in compression at different strain rates and under creep to cover its entire time-dependent behaviour. This information was used in a user subroutine in a finite element model to predict how the viscoplastic behaviour affects the stress redistribution around a fibre break. This redistribution was used as input for the KU Leuven fibre break model, which then predicts how the fibre break development changes over 109 s (31.7 years). When the model is held at a constant displacement corresponding to 90-94% of the mean failure strain, we observe a gradual increase in the fibre break density over 109 s. None of the 20 simulations per strain level predict failure within this time period. When the displacement was held at 96% and 98% of the mean failure strain, the fibre break density increased by 25% and 35%, respectively. About 20% and 50% of the simulations at this strain level caused failure before the 109 s was reached (see Fig. 1). This failure strain level, however, was already within the scatter on the mean failure strain, so some simulations failed before stress relaxation even started. These results confirm that UD composites can display stress relaxation failures, but only when the load is close to the mean failure strain. Follow-up studies should focus on creep failure, which is likely to be more severe than stress relaxation failure, and experimental validation of these findings.