The general equations of asymmetric theory of elasticity with the constraint rotation are considered in the sphere of three-dimensional thin shell. The interior iterational process and micropolar boundary layers are constructed by applying the asymptotic method. It is shown that both boundary layers - plane and antiplane, are of mixed force - momental character. The mating of the interior problem and the boundary value problems are studied for the satisfaction of three-dimensional boundary conditions on the lateral surface of the shell. In the result of this research, the boundary conditions for the interior micropolar problem and the separate boundary conditions for micropolar boundary layers are obtained.
   On the basis of the asymptotic method, the general applied two-dimensional theory of micropolar shells with the constraint rotation is constructed.