Thin-film field-effect transistors are essential elements of stretchable electronic devices for wearable electronics. All of the materials and components of such transistors need to be stretchable and mechanically robust. Although there has been recent progress towards stretchable conductors, the realization of stretchable semiconductors has focused mainly on strain-accommodating engineering of materials, or blending of nanofibres or nanowires into elastomers. An alternative approach relies on using semiconductors that are intrinsically stretchable, so that they can be fabricated using standard processing methods. Molecular stretchability can be enhanced when conjugated polymers, containing modified side-chains and segmented backbones, are infused with more flexible molecular building blocks. Here we present a design concept for stretchable semiconducting polymers, which involves introducing chemical moieties to promote dynamic non-covalent crosslinking of the conjugated polymers. These non-covalent crosslinking moieties are able to undergo an energy dissipation mechanism through breakage of bonds when strain is applied, while retaining high charge transport abilities. As a result, our polymer is able to recover its high field-effect mobility performance (more than 1 square centimetre per volt per second) even after a hundred cycles at 100 per cent applied strain. Organic thin-film field-effect transistors fabricated from these materials exhibited mobility as high as 1.3 square centimetres per volt per second and a high on/off current ratio exceeding a million. The field-effect mobility remained as high as 1.12 square centimetres per volt per second at 100 per cent strain along the direction perpendicular to the strain. The field-effect mobility of damaged devices can be almost fully recovered after a solvent and thermal healing treatment. Finally, we successfully fabricated a skin-inspired stretchable organic transistor operating under deformations that might be expected in a wearable device.