  Using the Walecka model, we investigate theoretically whether an omega meson
is bound to finite nuclei. We study several nuclei from ^{6}He to ^{208}Pb, and
compare the results with those in the quark-meson coupling (QMC) model. Our
calculation shows that deeper omega-nucleus bound states are predicted in the
Walecka model than in QMC. One can expect to detect such bound states in the
proposed experiment involving the (d,^3He) reaction at GSI.
