Many self-healing materials have been developed, but very few self-healing structures. We designed a structure in the form of a cylinder required to resist bending. Taking inspiration from plant stems, it has a cellular structure including longitudinal vascular channels for the delivery of healing agents. The structure was found to be capable of absorbing energy effectively, by deformation and fracture of cell walls. The introduction of healing agents (a two-part liquid adhesive) into the vascular channels allowed fractured cell walls to be repaired. The resulting structure was capable of near-perfect self-healing, restoring its original mechanical properties even after significant damage. A computer simulation (finite element analysis) successfully predicted the earlystage deformation and the initiation of damage. We advocate this structurelevel approach as a more appropriate way to introduce self-repair into engineering systems.