  We study Green functions for the pressure of stationary Stokes systems in a
(possibly unbounded) domain $\Omega\subset \mathbb{R}^d$, where $d\ge 2$. We
construct the Green function when coefficients are merely measurable in one
direction and have Dini mean oscillation in the other directions, and $\Omega$
is such that the divergence equation is solvable there. We also establish
global pointwise bounds for the Green function and its derivatives when
coefficients have Dini mean oscillation and $\Omega$ has a $C^{1,\rm{Dini}}$
boundary. Green functions for the flow velocity of Stokes systems are also
considered.
