The mean-free path $L_{\text{eff}}$ is calculated for a circular shell geometry under the assumptions of (i) billiard scattering and (ii) diffusive scattering. Similarly to a spherical shell geometry, $L_{\text{eff}}$ displays qualitatively different behavior on the shell thickness D for the two models. Whereas, for the billiard model $L_{\text{eff}}=\pi D/2$ , the mean-free path in the diffusive scattering case is a complicated function involving complete and incomplete elliptic integrals of the first, second, and third kinds. Nevertheless, a linear combination of D and $D\ln (R/2D)$ , where R is the outer circle radius, is shown to capture the functional dependence of $L_{\text{eff}}$ in the diffusive scattering case remarkably well over almost the entire parameter range. Hopefully, future experiments on single and well-controlled dielectric-core–metal-shell nanowires could differentiate between the two models.