[en] We present our recent analysis of the total reaction cross sections, σ_R, of unstable nuclei and discuss their sensitivity to the neutron-skin thickness. The σ_R is calculated with the Glauber model using projectile densities obtained with the Skyrme-Hartree-Fock method on the three-dimensional coordinate space. We cover 91 nuclei of O, Ne, Mg, Si, S, Ca, and Ni isotopes. Defining a reaction radius, a_R = √σ_R/π, to characterize the nuclear size and target (proton or "1"2C) dependence, we see the "1"2C target probes the matter radius while the proton target is sensitive to the skin-thickness. We find an empirical formula for expressing a_R with the point matter radius and the skin thickness, which can be used to determine the skin thickness. (author)