Recent biomedical hydrogels applications require the development of nanostructures with controlled diameter and adjustable mechanical properties. Here we present a technique for the production of flexible nanofilaments to be used as drug carriers or in microfluidics, with deformability and elasticity resembling those of long DNA chains. The fabrication method is based on the core-shell electrospinning technique with core solution polymerisation post electrospinning. Produced from the nanofibers highly deformable hydrogel nanofilaments are characterised by their Brownian motion and bending dynamics. The evaluated mechanical properties are compared with AFM nanoindentation tests.