This paper describes the development and application of inflow and outflow boundary conditions (BCs) for the material point method (MPM) in order to simulate fluid flow problems. This corresponds to velocity and pressure controlled BCs. Due to the coupled Lagrangian and Eulerian description of the fluid motion in MPM it is necessary to add and remove material points, with appropriate kinematic properties, to and from the computational domain. The newly-developed BCs have been used to simulate uniform open channel flow and the phenomenon of free overfall in open channels, which is transient conditions leading to non-uniform flow due to a sudden bed level drop. It is shown that the numerical results predict well the flow geometry including end depth ratio, pressure distribution and accelerations, therefore the velocities and displacements.