The endosomal sorting complex required for transport (ESCRT)-III complex, capable of polymerization and remodeling, participates in abscission of the intercellular membrane bridge connecting two daughter cells at the end of cytokinesis. Here, we integrate quantitative imaging of ESCRT-III during cytokinetic abscission with biophysical properties of ESCRT-III complexes to formulate and test a computational model for ESCRT-mediated cytokinetic abscission. We propose that cytokinetic abscission is driven by an ESCRT-III fission complex, which arises from ESCRT-III polymerization at the edge of the cytokinetic midbody structure, located at the center of the intercellular bridge. Formation of the fission complex is completed by remodeling and breakage of the ESCRT-III polymer assisted by VPS4. Subsequent spontaneous constriction of the fission complex generates bending deformation of the intercellular bridge membrane. The related membrane elastic force propels the fission complex along the intercellular bridge away from the midbody until it reaches an equilibrium position, determining the scission site. Membrane attachment to the dome-like end-cap of the fission complex drives membrane fission, completing the abscission process. We substantiate the model by theoretical analysis of the membrane elastic energy and by experimental verification of the major model assumptions.