Giant bilayer vesicles were reconstituted from several lipids and lipid/cholesterol (CHOL) mixtures: stearolyloleoylphosphatidylcholine (SOPC), bovine sphingomyelin (BSM), diarachidonylphosphatidylcholine (DAPC), SOPC/CHOL, BSM/CHOL, DAPC/CHOL, and extracted red blood cell (RBC) lipids with native cholesterol. Single-walled vesicles were manipulated by micropipette suction and several membrane material properties were determined. The properties measured were the elastic area compressibility modulus K, the critical areal strain alpha c, and the tensile strength tau lys, from which the failure energy or membrane toughness Tf was calculated. The elastic area expansion moduli for these lipid and lipid/cholesterol bilayers ranged from 57 dyn/cm for DAPC to 1,734 dyn/cm for BSM/CHOL. The SOPC/CHOL series and RBC lipids had intermediate values. The results indicated that the presence of cholesterol is the single most influential factor in increasing bilayer cohesion, but only for lipids where both chains are saturated, or mono- or diunsaturated. Multiple unsaturation in both lipid chains inhibits the condensing effect of cholesterol in bilayers. The SOPC/CHOL system was studied in more detail. The area expansion modulus showed a nonlinear increase with increasing cholesterol concentration up to a constant plateau, indicating a saturation limit for cholesterol in the bilayer phase of approximately 55 mol% CHOL. The membrane compressibility was modeled by a property-averaging composite theory involving two bilayer components, namely, uncomplexed lipid and a lipid/cholesterol complex of stoichiometry 1/1.22. The area expansion modulus of this molecular composite membrane was evaluated by a combination of the expansion moduli of each component scaled by their area fractions in the bilayer. Bilayer toughness, which is the energy stored in the bilayer at failure, showed a maximum value at approximately 40 mol% CHOL. This breakdown energy was found to be only a fraction of the available thermal energy, implying that many molecules (approximately 50-100) may be involved in forming the defect structure that leads to failure. The area expansion modulus of extracted RBC lipids with native cholesterol was compared with recent measurements of intact RBC membrane compressibility. The natural membrane was also modeled as a simple composite made up to a compressible lipid/cholesterol matrix containing relatively incompressible transmembrane proteins. It appears that the interaction of incompressible proteins with surrounding lipid confers enhanced compressibility on the composite structure.