Needle assemblies with valves and related methods are disclosed. An exemplary needle assembly includes a needle hub with a needle attached to a distal end of the needle hub and a catheter hub having a wall structure defining an interior cavity and a catheter tube extending distally therefrom having the needle projecting through the catheter tube. A valve with a cylindrical walled structure and a disc with a plurality of slits and flaps are located in the interior cavity of the catheter hub in which the cylindrical walled structure defines an open proximal end. A plurality of flexible ribs can be included and connect to an interior wall surface of the cylindrical walled structure and the disc with an actuator disposed inside the interior cavity of the catheter hub and having a distal end sized and shaped to project into the open proximal end of the valve.
