One of the major challenges in the field of biomaterials engineering is the replication of the non-linear elasticity observed in soft tissues. In the present study, non-linearly elastic biomaterials were successfully fabricated from a chemically cross-linked elastomeric poly (glycerol sebacate) (PGS) and thermoplastic poly(L-lactic acid) (PLLA) using the core/shell electrospinning technique. The spun fibrous materials, containing a PGS core and PLLA shell, demonstrated J-shaped stress-strain curves, and having ultimate tensile strength, rupture elongation, and stiffness constants respectively comparable to muscle tissue properties. In vitro evaluations also showed that PGS/PLLA fibrous biomaterials possess excellent biocompatibility, capable of supporting human stem-cell-derived cardiomyocytes over several weeks in culture. Therefore, the core/shell electrospun elastomeric materials provide a new potential scaffold to support cells in the therapy of a wide range of soft tissues exposed to cyclic deformation, such as tendon, ligament, cardiac or smooth muscle and lung epithelium. (c) 2013 Published by Elsevier Ltd.