A method of treating glaucoma in an eye utilizing an implant is disclosed. The implant comprises an elastomeric plate having first and second surfaces and an non-valved elastomeric drainage tube. The plate is positioned over a sclera of said eye beneath Tenon's capsule, such that a portion of the plate extends into the anterior segment of the eye. The first end of said elastomeric drainage tube is open to said second surface of said plate. The second end of said drainage tube is tunneled through the sclera and cornea and inserted into the anterior chamber of said eye. Fluid communication is provided between said anterior chamber and a scar tissue bleb which forms around said implant. Preferably, a portion of the scar tissue bleb extends into the anterior segment of the eye and a portion of the scar tissue bleb extends into the posterior segment of the eye.