  This paper presents results of three-dimensional direct numerical simulations
(DNS) and global linear stability analyses (LSA) of a viscous incompressible
flow past a finite-length cylinder with two free flat ends. The cylindrical
axis is normal to the streamwise direction. The work focuses on the effects of
aspect ratios (in the range of $0.5\leq \rm{\small AR} \leq2$, cylinder length
over diameter) and Reynolds numbers ($Re\leq1000$ based on cylinder diameter
and uniform incoming velocity) on the onset of vortex shedding in this flow.
All important flow patterns have been identified and studied, especially as
$\rm{\small AR}$ changes. The appearance of a steady wake pattern when
$\rm{\small AR}\leq1.75$ has not been discussed earlier in the literature for
this flow. LSA based on the time-mean flow has been applied to understand the
Hopf bifurcation past which vortex shedding happens. The nonlinear DNS results
indicate that there are two vortex shedding patterns at different $Re$, one is
transient and the other is nonlinearly saturated. The vortex-shedding
frequencies of these two flow patterns correspond to the eigenfrequencies of
the two global modes in the stability analysis of the time-mean flow. Wherever
possible, we compare the results of our analyses to those of the flows past
other short-$\rm{\small AR}$ bluff bodies in order that our discussions bear
more general meanings.
