This paper describes the synthesis and characterization of a class of highly stretchable and degradable semiconducting polymers. These materials are multi-block copolymers (BCPs) in which the semiconducting blocks are based on the diketopyrrolopyrrole (DPP) unit flanked by furan rings and the insulating blocks are poly(ε-caprolactone) (PCL). The combination of stiff conjugated segments with flexible aliphatic polyesters produces materials that can be stretched >100%. Remarkably, BCPs containing up to 90 wt% of insulating PCL have the same field-effect mobility as the pure semiconductor. Spectroscopic (ultraviolet-visible absorption) and morphological (atomic force microscopic) evidence suggests that the semiconducting blocks form aggregated and percolated structures with increasing content of the insulating PCL. Both PDPP and PCL segments in the BCPs degrade under simulated physiological conditions. Such materials could find use in wearable, implantable, and disposable electronic devices.