Abstract: The present invention provides microfluidic devices constructed from four layers. The layers include a rigid substrate layer, a patterned rigid layer having thickness t, a patterned elastomeric layer having thickness greater than t, and a rigid support layer. Microfluidic structures in the devices are defined by the alignment of openings in the patterned rigid layer and the patterned elastomeric layer. The rigid support layer, rigid substrate layer, and patterned rigid layer may be made of any rigid material, including but not limited to plastic or silicon-containing materials, such as glass, quartz, or SiO2-coated materials. Similarly, the patterned elastomeric layer may be made of any elastomeric material, including but not limited to polydimethylsiloxanes, polymethylmethacrylates, perfluoropolyethers, or combinations thereof. Microfluidic devices according to the present invention may include sensors or sensor arrays.