Mass transfer properties of the Soviet membrane oxygenator, MOCT, are tested. The liquid chambers of the oxygenator are made of disk membranes separating the moving blood from gas chambers. Processes of transportation and saturation of the blood film with oxygen are described by the simultaneous solution of the hydrodynamic and diffusion problem that is complicated by the chemical reaction. To derive approximate analytical solution the concept of a spreading front separating the area of the saturated blood layer from the venous area is applied. The expression for the thickness of the saturated layer and the oxygen flow to the blood is deduced as a function of the following parameters: membrane permeability, blood output, hemoglobin concentration, etc. The analytical solution is found to be satisfactory in describing experimental data obtained in the course of laboratory, clinical and biomedical tests.