The theory of distributions in non-Riemannian spaces is used to obtain exact static thin domain wall solutions of Einstein-Cartan equations of gravity. Curvature $ \delta $-singularities are found while Cartan torsion is given by Heaviside functions. Weitzenb\"{ o}ck planar walls are caracterized by torsion $\delta$-singularities and zero curvature. It is shown that Weitzenb\"{ o}ck static thin domain walls do not exist exactly as in general relativity. The global structure of Weitzenb\"{ o}ck nonstatic torsion walls is investigated.
Categories: gr-qc