Herein, we introduce a flexible, biocompatible, robust and conductive electrospun fiber mat as a substrate for flexible and stretchable electronic devices for various biomedical applications. To impart the electrospun fiber mats with electrical conductivity, poly(3,4‐ethylenedioxythiophene) (PEDOT), a conductive polymer, was interpenetrated into nitrile butadiene rubber (NBR) and poly(ethylene glycol)dimethacrylate (PEGDM) crosslinked electrospun fiber mats. The mats were fabricated with tunable fiber orientation, random and aligned, and displayed elastomeric mechanical properties and high conductivity. In addition, bending the mats caused a reversible change in their resistance. The cytotoxicity studies confirmed that the elastomeric and conductive electrospun fiber mats support cardiac cell growth, and thus are adaptable to a wide range of applications, including tissue engineering, implantable sensors and wearable bioelectronics.