We study Green functions for the pressure of stationary Stokes systems in a (possibly unbounded) domain $Omegasubset mathbb{R}^d$, where $dge 2$. 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.
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