Here we describe a simple yet efficient approach to making through-holes in a bound polydimethylsiloxane membrane for use in 3D microfluidic applications. Localized tearing of an elastomeric membrane is achieved by ripping an elastomeric stamp that is bound to the membrane by posts at desired regions. The tears in the membrane are confined by the underlying channel architecture of the substrate to which the membrane is bound. By varying the membrane thickness and channel dimensions, holes of different sizes can be obtained. This high-throughput method of generating through-holes will enable the design of complex microfluidic devices that require crossing of channel networks.