Graft-host mechanical mismatch has been a longstanding issue in clinical applications of synthetic scaffolds for soft tissue regeneration. Although numerous efforts have been devoted to resolve this grand challenge, the regenerative performance of existing synthetic scaffolds remains limited by slow tissue growth (comparing to autograft) and mechanical failures. We demonstrate a class of rationally designed flexible network scaffolds that can precisely replicate nonlinear mechanical responses of soft tissues and enhance tissue regeneration via reduced graft-host mechanical mismatch. Such flexible network scaffold includes a tubular network frame containing inversely engineered curved microstructures to produce desired mechanical properties, with an electrospun ultrathin film wrapped around the network to offer a proper microenvironment for cell growth. Using rat models with sciatic nerve defects or Achilles tendon injuries, our network scaffolds show regenerative performances evidently superior to that of clinically approved electrospun conduit scaffolds and achieve similar outcomes to autologous nerve transplantation in prevention of target organ atrophy and recovery of static sciatic index.