  We study the hadronic production of $B_s$ and $B_s^*$ mesons within the
fixed-flavor-number scheme, in which the dominant gluon-gluon fusion mechanism
is dealt with by using the complete $\alpha_s^4$ approach. Main theoretical
uncertainties for $B_s$ and $B_s^*$ production at TEVATRON and LHC are
presented. It is found that when $m_s$ increases by steps of 0.1 GeV, the
integrated cross section of $B^{(*)}_s$ decreases by $80%-100%$, when $m_b$
increases by steps of 0.1 GeV, it changes to be $\sim 10%$. While the
uncertainties caused by the parton distribution function and the factorization
scale varies within the region of 1/5 to 1/3. Considering possible kinematic
cut on the transverse momentum and the rapidity cut for the detectors at
TEVATRON and LHC, we also make estimations on the $B_s$ and $B_s^*$ production
with various kinematic cuts.
