The tensile strength of single cellulose acetate electrospun fibers is determined through sonication-induced fragmentation in water using a model previously developed by Terentjev and co-workers. The fragmentation of the electrospun fibers results in a gradual shortening of their length until a constant modal length is achieved. A single electrospun CA fiber tensile strength of approximate to 150 MPa (55-280 MPa) is determined based on fracture statistics. It is also observed that the fragmented fibers show bunches of nanofilaments at their ends with similar diameters to those of round structures observed in the cross-section of the initial electrospun fibers (approximate to 38 nm). The sonication of these nanofilaments gives rise to spherical particles with similar diameter dimensions, which allows the estimation of a value of the tensile strength of the order of 2 MPa for these nanostructures. The aggregation and the alignment of the nano filaments inside the electrospun fiber should be the source of its higher strength value.