Conventional photolithography uses rigid photomasks of fused quartz and high-purity silica glass plates covered with patterned microstructures of an opaque material. We introduce new, transparent, elastomeric molds (or stamps) of poly(dimethylsiloxane) (PDMS) that can be employed as photomasks to produce the same resist pattern as the pattern of the recessed (or non-contact) regions of the stamps, in contrast to other reports in the literature of using PDMS masks to generate edge patterns. The exposure dose of the non-contact regions with the photoresist through the PDMS is lower than that of the contact regions. Therefore, we employ a difference in the effective exposure dose between the contact and the non-contact regions through the PDMS stamp to generate the same pattern as the PDMS photomask. The photomasking capability of the PDMS stamps, which is similar to rigid photomasks in conventional photolithography, widens the application boundaries of soft-contact optical lithography and makes the photolithography process and equipment very simple. This soft-contact optical lithography process can be widely used to perform photolithography on flexible substrates, avoiding metal or resist cracks, as it uses soft, conformable, intimate contact with the photoresist without any external pressure. To this end, we demonstrate soft-contact optical lithography on a gold-coated PDMS substrate and utilized the patterned Au/PDMS substrate with feature sizes into the nanometer regime as a top electrode in organic light-emitting diodes that are formed by soft-contact lamination.