  In the last decade the CDF experiment at the Tevatron clearly demonstrated
that it is possible to study extensively heavy flavour physics in hadron
collisions and achieve remarkable results, competitive and complementary to
$B$-factories. In this paper we report on the indirect searches for physics
beyond the standard model via measurements of rare $b$-hadron decays. The final
limits, based on the analysis of the full CDF data set, on the branching
fraction of the $B^0_{(s)}$ decay into a pair of muons are presented and
discussed. Moreover we review the latest measurements, with 6.8 fb$^{-1}$ of
collected data, of the total and differential branching fractions and angular
observables of rare $b$-hadron decays proceeding via the flavour-changing
neutral-current process $b \rightarrow s \mu^+ \mu^-$. PACS numbers: 13.20.He,
13.30.-a, 12.15.Mn
