An elastomeric valve includes a barrel having one or more walls defining an interior fluid pathway. The barrel is deformable between a non-deformed state and a deformed state. The elastomeric valve further includes a gate assembly of two or more gate elements forming a tapering volume projecting into the fluid pathway from the one or more walls of the barrel. In at least some examples, each gate element joins the barrel at a reduced cross-section that forms a hinge of that gate element. The two or more gate elements interface with each other along one or more gate boundaries to collectively block the fluid pathway in the non-deformed state and separate from each other along the one or more gate boundaries in the deformed state to permit fluid flow through the gate assembly.