TECHNOLOGY FOCUS - CHEMICAL ENGINEERING - Preferred Apparatus: A reaction container (1) or reaction tube having several slits made from a porous component, a pore board, a net-like component and dividing wall, is used for performing the reaction. A filled layer, which is supported with substance of a grain-shape, debris-like, or ring-shape is provided in the reaction container. Several shelves are provided in the reaction container in inclined and/or horizontal direction. The shelf is pore board, minute net-like component, bubble-cap or other gas-liquid-contact unit. The reaction container has thin tube having internal diameter of less than 50 mm, and a mixed-liquid unit in its interior. The reaction container has several supply holes through which vaporized alcohol (8) is supplied at the vicinity of oil and fat surface. The reaction container has a fluid bed formed by arranging the mixture of fat and oils and alcohol.    TECHNOLOGY FOCUS - INORGANIC CHEMISTRY - Preferred Catalyst: The solid catalyst is alloy and/or a metal, and has grain shape or debris shape. The solid catalyst is arranged at the shelf surface of the reaction container. One or whole portion of solid catalyst contains iron, nickel, molybdenum, cobalt, copper, zinc, aluminum, lead and/or tin, their alloy or compound formed using the elements.    TECHNOLOGY FOCUS - ORGANIC CHEMISTRY - Preferred Condition: Oil and fat, and alcohol in the form of superheated steam are reacted at 350-250 degrees C under atmospheric-pressure vicinity of 0.101-0.15 MPa.Preferred Composition: The amount of alcohol is more than thrice of theoretical chemistry equivalent with respect to oil and fat during reaction.Preferred Process: The vaporized alcohol is supplied to oil and fat in reaction container through cellular apparatus, such as nozzle, pore board, pore component, or ultrasonic component. Alcohol or vaporized alcohol is introduced to gas-liquid mixing apparatus, such as gas-liquid mixing pump, with oil and fats, in the form of granule having particle size of 100 microns or less. The oil and fat of granular form of aerosol vicinity is obtained using an atomization apparatus having an ultrasonic unit. The fatty acid ester is manufactured by repeating the reaction of fat and oils with alcohol. The substance containing the reaction product produced when vaporization alcohol passes through the inside of oil and fat, the reaction product produced in oil-and-fat surface (the foam layer of an oil-and-fat surface is contained), and/or oil-and-fat surface vicinity space is acquired with excess vaporization alcohol, as the gaseous mixture phase or dispersed phase in excess vaporization alcohol. The mixture of reaction-product (fatty acid ester, glycerol (4) and incomplete reaction material), and unreacted substance (oil and fat and alcohol) acquired from reaction container is separated to fatty acid ester, glycerol, alcohol, and oil and fat by the gravity-separation-distillation method. Alcohol and oil and fat are again used as a raw material. One or whole of the incomplete reaction material is also separated further, and used as a raw material again. The excess vaporized alcohol containing reaction product, or reaction product, and unreacted oil and fat, are introduced to distilling column having predetermined number of stages. The unreacted oil and fat, and reaction product are separated from excess vaporized alcohol as condensate based on boiling point difference with alcohol in the column. The condensate is separated based on specific gravity difference or boiling point difference. The vaporized alcohol is continuously introduced to one side of reaction container, and oil and fat is introduced on other side of reaction container.Preferred Compound: The alcohol has structure of formula: R-OH, where R is 1-5C alkyl, preferably methyl or ethyl, more preferably methyl.Preferred Oil: Oil and fat is waste oil and fat, and/or waste edible oil, preferably animal fats and oils, or vegetable oil. The vegetable oil is palm oil and/or rapeseed oil. The vegetable oil is rough palm oil having pressed oil.    TECHNOLOGY FOCUS - ORGANIC CHEMISTRY - Preferred Catalyst: The solid catalyst is alloy and/or a metal, and has grain shape or debris shape. The solid catalyst is arranged at the shelf surface of the reaction container. One or whole portion of solid catalyst contains iron, nickel, molybdenum, cobalt, copper, zinc, aluminum, lead and/or tin, their alloy or compound formed using the elements. EXAMPLE - Rapeseed oil (200 ml) having dynamic viscosity of 52.3 mm2/second was supplied to an autoclave under pressure of 5 MPa at 250 degrees C. Methanol was supplied, and reaction was carried out for 60 minutes to obtain fatty acid ester having dynamic viscosity of 7-9 mm2/second.