  We estimate, for the first time, the $\Upsilon$ and $\eta_b$ mass shifts in
symmetric nuclear matter. The estimate for the $\Upsilon$ is made using an
SU(5) effective Lagrangian, studying the $BB$, $BB^*$, and $B^*B^*$ meson loop
contributions for the self-energy. As a result, we include only the $BB$ meson
loop contribution as our minimal prediction. As for the $\eta_b$, we include
only the $BB^*$ meson loop contribution in the self-energy to be consistent
with the minimal prediction for the $\Upsilon$ mass shift. The in-medium masses
of the $B$ and $B^{*}$ mesons appearing in the self-energy loops are calculated
by the quark-meson coupling model. Form factors are used to regularize the loop
integrals with a wide range of the cutoff mass values. A detailed analysis on
the $BB$, $BB^{*}$, and $B^{*}B^{*}$ meson loop contributions for the
$\Upsilon$ mass shift is made by comparing with the corresponding $DD, DD^*$,
and $D^*D^*$ meson loop contributions for the $J/\Psi$ mass shift. Based on the
analysis for the $\Upsilon$, our prediction for the $\eta_b$ mass shift is made
on the same footing as that for the $\Upsilon$, namely including only the
$BB^*$ meson loop. The $\Upsilon$ mass shift is predicted to be -16 to -22 MeV
at the symmetric nuclear matter saturation density with the cutoff mass values
in the range 2000 - 6000 MeV using the $\Upsilon BB$ coupling constant
determined by the vector meson dominance model, while the $\eta_b$ mass shift
is predicted to be -75 to -82 MeV with the SU(5) universal coupling constant
determined by the $\Upsilon BB$ coupling constant and for the same range of the
cutoff mass values.
