Polydimethylsiloxane (PDMS) fibers with unexpected elasticity were prepared by a modified core-shell electrospinning method using a commercially-available liquid PDMS precursor (Sylgard 184) and polyvinylpyrrolidone (PVP) as core and sheath materials, respectively. The liquid PDMS precursor was crosslinked in situ to form a solid core when the newly-electrospun core-sheath nanofibers were deposited onto a hot-plate electrode collector. After dissolving the PVP sheath layer off the fibers, net PDMS fibers showed larger average diameter than core-sheath fibers, with an average diameter around 1.35 mu m. The tensile properties of both single fibers and fibrous mats were measured. Single PDMS fibers had a tensile strength and elongation at break of 6.0 MPa and 212%, respectively, which were higher than those of PDMS cast film (4.9 MPa, 93%). The PDMS fiber mat had larger elongation at break than the single PDMS fibers, which can be drawn up to 403% their original length. Cyclic loading tests indicated a Mullin effect on the PDMS fiber mats. Such a superior elastic feature was attributed to the PDMS molecular orientation within fibers and the randomly-orientated fibrous structure. Highly-elastic, ultrafine PDMS fibers may find applications in strain sensors, biomedical engineering, wound healing, filtration, catalysis, and functional textiles.