Substrates or encapsulants in soft and stretchable formats are key components for transient, bioresorbable electronic systems; however, elastomeric polymers with desired mechanical and biochemical properties are very limited compared to non-transient counterparts. Here, we introduce a bioresorbable elastomer, poly(glycolide-co-ε-caprolactone) (PGCL), that contains excellent material properties including high elongation-at-break (< 1300%), resilience and toughness, and tunable dissolution behaviors. Exploitation of PGCLs as polymer matrices, in combination with conducing polymers, yields stretchable, conductive composites for degradable interconnects, sensors, and actuators, which can reliably function under external strains. Integration of device components with wireless modules demonstrates elastic, transient electronic suture system with on-demand drug delivery for rapid recovery of post-surgical wounds in soft, time-dynamic tissues.