The intrinsic scatter in tensile properties of unidirectional (UD) carbon/epoxy composites is due to several factors, including variability in fibre strength and fibre volume fraction at the local microscopic level. A model included in a multiscale finite element process, previously developed to simulate fibre failure in composite laminates but having little variation in fibre strength and local fibre volume fraction, has been extended to cover the effects of such material variations. The present study investigates the effects of the variability in material properties which can occur in real UD composite materials subjected to monotonic increasing and sustained loadings. This latter case is one of the originalities of this study. In the interval of variation studied for the Weibull parameters of fibre strength and fibre volume fraction, the mean and standard deviation of the failure stress are never strongly affected. Concerning the time-to-failure, its mean and its standard deviation increase strongly if the mean of fibre volume fraction increases and if the standard deviation of the fibre strength decreases. The standard deviation of local fibre volume fraction was found to have only a secondary effect on failure stress and time-to-failure. Another original and important result concerns the scatter in the time-to-failure of composites due to the level of applied sustained loading.