Fluidic transport through nanochannels offers new opportunities to probe fundamental nanoscale transport phenomena and to develop tools for manipulating DNA, proteins, small molecules and nanoparticles. The small size of nanofabricated devices and the accompanying increase in the effect of surface forces, however, pose challenges in designing and fabricating flexible nanofluidic systems that can dynamically adjust their transport characteristics according to the handling needs of various molecules and nanoparticles. Here, we describe the use of nanoscale fracturing of oxidized poly(dimethylsiloxane) to conveniently fabricate nanofluidic systems with arrays of nanochannels that can actively manipulate nanofluidic transport through dynamic modulation of the channel cross-section. We present the design parameters for engineering material properties and channel geometry to achieve reversible nanochannel deformation using remarkably small forces. We demonstrate the versatility of the elastomeric nanochannels through tuneable sieving and trapping of nanoparticles, dynamic manipulation of the conformation of single DNA molecules and in situ photofabrication of movable polymeric nanostructures.