Cylindrical soft magnetic Co films, nanostructured with a grain size of 1-2 nm and between ≈1.3 and 90 nm in thickness, were produced by the pulsed laser deposition technique. These films showed a magnetostrictive property. The magnetoelastic inverse Wiedemann effect, or IWE, of longitudinal magnetization as a function of the circular applied magnetic field, M z -H φ , was measured. The IWE made it possible to explain the magnetization processes according to an initial reversible rotation of the magnetization followed by magnetic wall nucleation and propagation. A magnetization rotation model allowed us to compare the reversible part and the first irreversible magnetization processes corresponding to the IWE. In this way, the values of the helical magnetic anisotropy, K h , due to the helical stresses, σ h , generated by an applied torque to the films, were determined. A linear increase of the nucleating magnetic wall field, H N , with the applied torque, or with σ h , was observed. In addition, the IWE made it possible to establish the non-dependence of the saturation magnetostriction constant, λ s , on the sample thickness and to determine the value of this negative isotropic λ s ≈ −4.8 × 10 −6 .