Skin-like electronics that can adhere seamlessly to human skin or within the body are highly desirable for applications such as health monitoring, medical treatment, medical implants and biological studies, and for technologies that include human-machine interfaces, soft robotics and augmented reality. Rendering such electronics soft and stretchable-like human skin-would make them more comfortable to wear, and, through increased contact area, would greatly enhance the fidelity of signals acquired from the skin. Structural engineering of rigid inorganic and organic devices has enabled circuit-level stretchability, but this requires sophisticated fabrication techniques and usually suffers from reduced densities of devices within an array. We reasoned that the desired parameters, such as higher mechanical deformability and robustness, improved skin compatibility and higher device density, could be provided by using intrinsically stretchable polymer materials instead. However, the production of intrinsically stretchable materials and devices is still largely in its infancy: such materials have been reported, but functional, intrinsically stretchable electronics have yet to be demonstrated owing to the lack of a scalable fabrication technology. Here we describe a fabrication process that enables high yield and uniformity from a variety of intrinsically stretchable electronic polymers. We demonstrate an intrinsically stretchable polymer transistor array with an unprecedented device density of 347 transistors per square centimetre. The transistors have an average charge-carrier mobility comparable to that of amorphous silicon, varying only slightly (within one order of magnitude) when subjected to 100 per cent strain for 1,000 cycles, without current-voltage hysteresis. Our transistor arrays thus constitute intrinsically stretchable skin electronics, and include an active matrix for sensory arrays, as well as analogue and digital circuit elements. Our process offers a general platform for incorporating other intrinsically stretchable polymer materials, enabling the fabrication of next-generation stretchable skin electronic devices.