Abstract: 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.