A theory of resonant spin-dependent tunneling has been developed for symmetrical double-barrier structures grown of noncentrosymmetrical semiconductors. The dependence of the tunneling transparency on the spin orientation and the wave vector of electrons leads to (i) spin polarization of the transmitted carriers in an in-plane electric field and (ii) generation of an in-plane electric current under tunneling of spin-polarized carriers. These effects originated from spin-orbit coupling-induced splitting of the resonant level have been considered for double-barrier tunneling structures.