In this paper, we conduct a feasibility study to investigate the future potential of textile composites with shape memory alloys. Two different types of SMA-based textile composites are presented. First, a composite plate with embedded woven SMA layer is fabricated, and the stiffness tuning capability is evaluated by impact vibration tests. The results are not favorable, but may be improved by increasing the volume fraction of SMA, and by controlling the prestrain more accurately during the lamination process. The modeling and analysis methodology for woven SMA-based composites are briefly discussed. Then, the possibility of textile composites with SMA stitching is discussed, that is expected to give the composites multi-functions such as tunable stiffness, shape control and sensing capability, selectively distributed on demand.