Apparatus and methods are disclosed for maturing an elongate replacement tissue construct in vitro prior to use of the replacement construct in vivo as, for example, a ligament. The tissue is seeded with specific cells, exposed to a maturation fluid, and subjected to selected forces, which can include longitudinal stress (i.e. stressing the tissue along its elongate axis). The tissue is disposed in a maturation chamber that confines maturation fluid for introduction to the tissue. A first mounting element couples to a first end of the elongate biopolymer tissue and a second mounting element couples to a second end of the tissue such that the tissue extends along a longitudinal axis, and a force is applied to at least one of the mounting elements for longitudinally stressing the tissue. The foregoing apparatus and methods are intended to provide a replacement tissue that is more readily integrable in vivo, i.e., a tissue that more readily degrades, regenerates and remodels in vivo to produce a more durable and functional replacement tissue.