Glaucoma treatments 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 tissue to the anterior chamber of the eye. The drainage tube collapses upon 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. Delayed fluid communication between the outflow and inflow ends of the drainage tube permits a scar tissue bleb to form around the plate. The plate desirably has a peripheral ridge and 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.