Abstract: A bias-weaving machine is provided. In one embodiment, the bias-weaving machine includes a plurality of yarn carriers, each holding a yarn under tension that extends in a downstream direction towards a woven product. The yarn carriers are translatable in at least one direction other than the downstream direction. The apparatus further includes a plurality of reeds disposed to comb the yarns in a downstream direction. The reeds have a range of motion extending between positions upstream and downstream of the yarn carriers. Embodiment of this invention may advantageously be utilized to weave three-dimensional woven products, such as textile preforms for aerospace composites.