Planar glass membrane fibers (PGMFs) are of current interest owing to the fact that they combine the interesting dispersive properties of fibers with diffraction in one unbound transverse dimension. We study supercontinuum (SC) spectra generated in PGMFs and show that the underlying dynamics has similarities to bulk medium. At the same time, the rich dispersion properties of PGMFs open up new possibilities, including SC spectral shapes that do not occur in natural bulk media. In all cases, the SC spectra in PGMFs can be interpreted in detail using the effective-three-wave-mixing model originally developed for bulk media. (C) 2009 Optical Society of America.