A new algorithm to generate random spatial distributions of cylindrical fibres and spheres is developed based on a constrained optimization formulation. All filler particles are generated simultaneously within the specimen domain; subsequently their position is iteratively perturbed to remove particle overlapping. The algorithm is able to achieve volume fractions of up to 0.8 in the case of circular cylindrical fibres of equal diameter; the method can be applied to any statistical distribution of fibre diameters. The spatial distribution of fibres and spheres is analysed by plotting spatial statistical metrics; it is shown that the microstructures generated are spatially random and similar to those observed in real fibre composites. The algorithm is employed to effectively predict the transversely isotropic elastic, damping and plastic properties of a unidirectional fibre composite by analysis of an RVE of smaller size than previously reported.