A method of treating glaucoma in an eye utilizing an implanted shunt having an elastomeric plate and a non-valved elastomeric drainage tube. The plate is positioned over a sclera of the eye with an outflow end of the elastomeric drainage tube open to an outer surface of the plate. An inflow end of the drainage tube tunnels through the sclera and cornea to the anterior chamber of the eye. The drainage tube collapses upon initial insertion within an incision in the sclera and cornea, or at a kink on the outside of the incision, but has sufficient resiliency to restore its patency over time. The effect is a flow restrictor that regulates outflow from the eye until a scar tissue bleb forms around the plate of the shunt. The plate desirably has a peripheral ridge and a large number of fenestrations, and a longer suturing tab extending from one side of the plate to enhance visibility and accessibility when suturing the shunt to the sclera.
