We describe reshaping of active textiles actuated by bending of Janus fibres comprising both active and passive components. A great variety of shapes, determined by minimising the overall energy of the fabric, can be produced by varying bending directions determined by the orientation of Janus fibres. Under certain conditions, alternative equilibrium states, one absolutely stable and the other metastable coexist, and their relative energy may flip its sign as system parameters, such as the extension upon actuation, change. A snap-through reshaping in a specially structured textile reproduces the Venus flytrap effect.