  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.
