A theoretical model and an experiment are presented for determining the bending modulus of a bilayer vesicle membrane. The vesicle is held with a pipet having a radius between 1 and 2 microns, and the tension in the membrane is changed by changing the suction pressure. Then the vesicle membrane is deformed by aspirating it into a smaller pipet having a radius on the order of 0.5 microns. The relationship between the suction pressures in the two pipets is found to be linear, as predicted by the theoretical model. The curvature of the vesicle membrane at the pipet orifice and the bending modulus are found with the help of the model from the slope and the intercept of the linear experimental relationship between the suction pressures in the two pipets. The bending modulus for the two SOPC membranes studied in these experiments was found to be either 0.6 or 1.15 x 10(-19) J, which is similar to the values measured previously.