We describe a facile and simple stamping method to fabricate various cross-sectional shaped microfluidic channels in transparent polymer materials such as polydimethylsiloxane (PDMS), poly(methylmethacrylate) (PMMA), polystyrene (PS), and cyclic olefin copolymer (COC). First, microchannels of circular, rectangular, and triangular shape and different size were fabricated on a silicon wafer through an isotropic or anisotropic wet etching process, and the resultant microchannels on silicon wafers were transferred to PDMS through a replication technique. The produced PDMS with replicated convex microchannels served as a master mold. A variety of polymer solutions were pressed down against the PDMS master mold, and cured until the solvent was evaporated, generating circular, rectangular, and triangular shaped PDMS, PMMA, PS, and COC microchannels. The microchannels could be repeatedly prepared with a narrow standard deviation, thus demonstrating high reproducibility of the proposed method. The microchannel dimensions, shape, and surface roughness could be controlled by tuning the channel width of the mask, the wet etching direction, the etchant solution, and the concentration of KOH, respectively, when the microchannels were fabricated on a silicon wafer. This simple but efficient PDMS mold based stamping method can be widely used for fabricating different shaped microchannels on diverse polymer materials with high reproducibility, low cost, and high speed.