The spin-dependent tunneling phenomenon in symmetric and asymmetric resonant semiconductor heterostructures is employed in a theoretical study to investigate the output tunnel current polarization at zero magnetic field. A simple model of the resonant tunneling structures and a simple one-electron band approximation with spin-orbit interaction are used in this work. It is shown that asymmetry in the electron distribution at the electrode regions provides spin-polarized tunnel current. An approach to optimize this spin-dependent effect is explored theoretically. In asymmetric resonant tunneling structures, we estimate theoretically that the polarization can reach 40% with a moderate applied electric field.