A membrane assembly for vacuum bagging includes an elongate sheet of flexible material capable of being rolled up into a cylindrical configuration and unrolled from the cylindrical configuration into a flattened-out configuration, a bistable tape spring attached to or captured by the elongate sheet, and an inflatable tube attached to or captured by the elongate sheet. The bistable tape spring has a first stable state which is a straightened-out state, a second stable state which is a rolled-up state, and a transition state between the first and second stable states. The inflatable tube is sealed at one end and has an orifice at the other end for admission of a fluid therethrough for inflation of the inflatable tube.