Cell-size vesicles were made from amphiphilic diblock copolymers and characterized by micromanipulation. The average molecular weight of the base, synthetic polymer studied here, polyethyleneoxide-polyethylethylene (EO40-EE37), is several-fold greater than that of usual phospholipids of biomembranes. Both the membrane bending and area expansion moduli of electroformed polymersomes (polymer-based liposomes) fell within the range of lipid membrane measurements, but the giant polymersome's membrane proved to be almost an order of magnitude tougher, sustaining far greater areal strain before rupture. The polymersome membrane was also at least tenfold less permeable to water than common phospholipid bilayers. A rich range of vesicle shapes, as well as encapsulation of oxygen-binding proteins, and capabilities to mix the polymer with other amphiphiles and crosslink it, all suggest a new class of functional, biomimetic capsules based on block copolymer chemistry.