The disclosed subject matter relates to a multilayer stretchy drawstring and methods of making the same. The drawstring of the disclosed subject matter is a stretched multilayer coextruded or laminated film that offers good balance between easy stretching at low strain and high strain hardening at high strain. The multilayer film includes a first layer of elastomeric polymer and second and third layers of thermoplastic polymer and is stretched beyond the deformation limit of the thermoplastic polymer and allowed to recover. This novel drawstring can be incorporated into a bag to enable the bag to be securely fitted to the upper portion of a trash container while not interfering with the intrinsic strength and operation of the drawstring.