We study regularity problem for the Stokes system (SS) and the Navier-Stokes equations (NSE) near boundary. For the steady-state case we obtained local estimates of the SS "without pressure" and as an application we prove the partial regularity up to the boundary for the stationary NSE in five dimension. For the non-stationary SS we constructed an example, which shows, unlike in the interior case,

H\"{o}lder continuity does not imply smoothness in the spatial variable near boundary. For the NSE We proved that weak solutions,

which is locally in $L^{p,q}$ with $3/p+n/q=1, q>n$ near boundary are regular up to the boundary. In three dimension we also observed

that "suitable weak solutions" of the NSE are regular near boundary if the scaled $L^{r,s}$-norm with $3/r+2/s=2, 2<s<\infty$ of the velocity is sufficiently small.