A glaucoma drainage device having an elastomeric plate and a non-valvedelastomericdrainage tube. The plate is positioned over a sclera of the eye with anoutflow end of theelastomeric drainage tube open to an outer surface of the plate. An inflow endof thedrainage tube tunnels through the sclera and cornea to the anterior chamber ofthe eye.The drainage tube collapses upon initial insertion within an incision in thesclera andcornea, or at a kink on the outside of the incision, but has sufficientresiliency to restoreits patency over time. The effect is a flow restrictor that regulates outflowfrom the eyeuntil a scar tissue bleb forms around the plate of the shunt.