Abstract: The present invention is directed to a method of producing fuel from vegetable or animal fat having a free fatty acid content by means of catalytic esterification reactions. The method includes esterification of free fatty acids at a higher temperature in a vacuum with one or more multivalent alcohols accompanied by solid neutral catalysts, which are present in a packing bed inside a reactor, whereby the fat travels from top to bottom in the reactor with the alcohol(s) running counter current and a mixture containing alcohol and water being removed from an upper part of the reactor by means of a vacuum effect. The present invention is also directed to the apparatus for implementing the methods disclosed.