Conductive electrodes and electric circuits that can remain active and electrically stable under large mechanical deformations are highly desirable for applications such as flexible displays, field-effect transistors, energy-related devices, smart clothing and actuators. However, high conductivity and stretchability seem to be mutually exclusive parameters. The most promising solution to this problem has been to use one-dimensional nanostructures such as carbon nanotubes and metal nanowires coated on a stretchable fabric, metal stripes with a wavy geometry, composite elastomers embedding conductive fillers and interpenetrating networks of a liquid metal and rubber. At present, the conductivity values at large strains remain too low to satisfy requirements for practical applications. Moreover, the ability to make arbitrary patterns over large areas is also desirable. Here, we introduce a conductive composite mat of silver nanoparticles and rubber fibres that allows the formation of highly stretchable circuits through a fabrication process that is compatible with any substrate and scalable for large-area applications. A silver nanoparticle precursor is absorbed in electrospun poly (styrene-block-butadiene-block-styrene) (SBS) rubber fibres and then converted into silver nanoparticles directly in the fibre mat. Percolation of the silver nanoparticles inside the fibres leads to a high bulk conductivity, which is preserved at large deformations (σ ≈ 2,200 S cm(-1) at 100% strain for a 150-µm-thick mat). We design electric circuits directly on the electrospun fibre mat by nozzle printing, inkjet printing and spray printing of the precursor solution and fabricate a highly stretchable antenna, a strain sensor and a highly stretchable light-emitting diode as examples of applications.