  We study classical dynamics of cylindrical membranes wrapped around the extra
compact dimension of a $(D+1)$-dimensional Riemann-Cartan spacetime. The
world-sheet equations and boundary conditions are obtained from the universally
valid conservation equations of the stress-energy and spin tensors.
Specifically, we consider membranes made of macroscopic matter with maximally
symmetric distribution of spin. In the narrow membrane limit, the dimensionally
reduced theory is obtained. It describes how effective strings couple to the
effective $D$-dimensional geometry. The striking coincidence with the string
theory $\sigma$-model is observed. In this correspondence, the string
background fields $G_{\mu\nu}$, $B_{\mu\nu}$, $A_{\mu}$ and $\Phi$ are related
to the metric and torsion of the Riemann-Cartan spacetime.
