We report a molecular simulation study of hydrodynamics in clay nanopores, with pore widths ranging from 2 to 9 nm. Understanding mass transfer through clay nanopores is necessary in many contexts such as groundwater hydrology, petroleum and gas reservoir engineering, as well as carbon dioxide sequestration or geological disposal of radioactive waste. Grand-canonical Monte Carlo simulations first allow us to determine the water content in the pores. We then analyze the structure and diffusion of confined water using equilibrium molecular dynamics (MD). Finally, nonequilibrium MD allow us to analyze the hydrodynamic behavior of the confined fluid and assess the relevance of continuum hydrodynamics to describe the flow under a pressure gradient. The Navier–Stokes equation, using the density and viscosity of the bulk fluid, provides a reasonable description of the flow provided that the pore width is larger than 3 nm and that a slip boundary condition is used. We determine a slip length of 2.1 Å at the clay surface. Although this value is small, neglecting slip in these nanopores results in large errors on the hydrodynamic flow. In the vicinity of the surface, the deviations from the prediction of the Navier–Stokes equation cannot be captured by a local viscosity determined from MD simulations.