A surgical implant device for treating glaucoma includes an elongate duct structure formed from a material comprising polyisobutylene and a glassy segment. The material of the elongate duct structure preferably has a general block structure with a central elastomeric polyolefinic block and thermoplastic end blocks (e.g., a triblock polymer backbone comprising polystyrene-polyisobutylene-polystyrene). The elongate duct structure provides a fluid passageway for diverting aqueous humor from the anterior chamber of the eye. Preferably, the elongate duct structure defines a lumen channel having an inside diameter between 0.05 mm and 0.3 mm. The material of the elongate duct structure is biocompatible and biostable. Moreover, the material will not encapsulate in the eye and thus provides an unobstructed flowpath that diverts aqueous humor from the anterior chamber. Different embodiments of the implant device divert the aqueous humor to different parts of the eye (e.g., a space between the conjuctiva and sclera, Schlemm's canal, or a fluid reservoir formed on a posterior surface of the eye).