Method and apparatus for producing biodiesel fuel, i.e., alkyl ester, from vegetable and/or animal oil. A transesterification catalyst is prepared in a base catalyst tank by spraying alkyl alcohol under pressure through jets at metal hydroxide pellets until the pellets have fully reacted with the alcohol. The oil is heated and transesterified in the presence of alkyl alcohol and the transesterification catalyst in a closed, recirculating transesterification flow system under slight cavitation to yield product alkyl ester and product glycerol. Cavitation is achieved by permitting air to enter the transesterification flow system through an adjustable air inlet valve. When permitted to stand, product alkyl ester forms an upper layer that is decanted and subjected to purification steps, to remove particulates and alkyl alcohol from the product alkyl ester, and a lower layer of product glycerol is drained away. Purification of the product alkyl ester preferably includes subjecting the product alkyl ester to an overhead water mist in a wash tank with simultaneous infusion of a stream of air bubbles. Alcohol vapor is reclaimed as liquid alcohol within an alcohol condenser and stored for reuse. If the oil contains free fatty acids, prior to transesterification, the oil is heated and the free fatty acids are esterified in the presence of an esterification catalyst and alkyl alcohol. For safety, baffles and explosion damper/flame arrestors are provided in locations where flammable vapors pose a risk.