Hydra regenerates one head when cut, but how forces shaping the head are coordinated remains unclear. Soft compression of Hydra 's head-regenerating tissues induces the formation of viable, two-headed animals. Compression creates new topological defects in the supracellular orientational order of muscular actin fibers, associated with additional heads. Theory supports that these defects organize muscle stresses required to shape the head. By compressing head-regenerating tissues along their body axis, we formed toroidal tissues, whose unique topology allows for the absence of defects. Toroids with no actin defects did not regenerate. Toroids with actin defects regenerated into viable toroidal animals with a bifurcated body. Topological defects in the actin orientational order are thus necessary for complete regeneration of Hydra , defining actin topological defects as mechanical organizers of morphogenesis.