Mechanical forces play an important role in shaping the organization of the extracellular matrix (ECM) in developing and mature tissues. The resulting organization gives the tissue its unique functional properties. Understanding how mechanical forces influence the alignment of the ECM is important in tissue engineering, where recapitulating the alignment of the native tissue is essential for appropriate mechanical anisotropy. In this work, a novel method was developed to create and stretch tubular cell sheets by seeding neonatal dermal fibroblasts onto a rotating silicone tube. We show the fibroblasts proliferated to create a confluent monolayer around the tube and a collagenous, isotropic tubular tissue over 4 weeks of static culture. These silicone tubes with overlying tubular tissue constructs were mounted into a cyclic distension bioreactor and subjected to cyclic circumferential stretch at 5% strain, 0.5 Hz for 3 weeks. We found that the tissue subjected to cyclic stretch compacted axially over the silicone tube in comparison to static controls, leading to a circumferentially aligned tissue with higher membrane stiffness and maximum tension. In a subsequent study, the tissue constructs were constrained against axial compaction during cyclic stretching. The resulting alignment of fibroblasts and collagen was perpendicular (axial) to the stretch direction (circumferential). When the cells were devitalized with sodium azide before stretching, similarly constrained tissue did not develop strong axial alignment. This work suggests that both mechanical stretching and mechanical constraints are important in determining tissue organization, and that this organization is dependent on an intact cytoskeleton.