An all-elastomer strain engineering approach, which uses patterned elastomer layers with tunable stiffnesses, can be used to create intrinsically stretchable transistor arrays with a device density of 340 transistors cm<
sup>
-2 <
/sup>
and strain insensitivity of less than 5% performance variation when stretched to 100% strain. Intrinsically stretchable electronics can form intimate interfaces with the human body, creating devices that could be used to monitor physiological signals without constraining movement. However, mechanical strain invariably leads to the degradation of the electronic properties of the devices. Here we show that strain-insensitive intrinsically stretchable transistor arrays can be created using an all-elastomer strain engineering approach, in which the patterned elastomer layers with tunable stiffnesses are incorporated into the transistor structure. By varying the cross-linking density of the elastomers, areas of increased local stiffness are introduced, reducing strain on the active regions of the devices. This approach can be readily incorporated into existing fabrication processes, and we use it to create arrays with a device density of 340 transistors cm<
sup>
-2<
/sup>
and a strain insensitivity of less than 5% performance variation when stretched to 100% strain. We also show that it can be used to fabricate strain-insensitive circuit elements, including NOR gates, ring oscillators and high-gain amplifiers for the stable monitoring of electrophysiological signals.