A breast pump includes a pump that produces both vacuum and pulsating pressure, at least one express kit, and hoses or the like for connecting the pump to the express kit. The express kit includes a manifold, a milk collection vessel, a rigid cup and a flexible liner. The liner is made of a pliable material, and includes a funnel and a throat. The inside surface of the funnel, which is between the liner and the cup when the liner is installed, has an optional honeycomb structure that creates a forced space between the liner and the cup, while maintaining some degree of flexibility. At the end of the liner inside the throat, a rigid insert or suitable bond maintains some rigidity inside the throat, supports the liner and creates a seal between the liner and the cup at the throat end of the liner.