Installation and method for producing fatty acid esters usable as fuel for which the installation includes a tank (10) containing oils and/or fats to be treated, a tank (11) containing light alcohol, pumps (3) and (4) feeding the materials to a tubular reaction vessel (30) having a winding configuration provided with a heater for internally maintaining a supercritical temperature with respect to the alcohol used and a pressure provided by the pumps, suitable for producing esterification and transesterification reactions, without the presence of catalysts of the oils and/or fats and alcohol, a heat exchanger (8) for heating the affluents and cooling the reaction effluents and a reaction effluent depressurization tank (21). The installation further has a stirrer (22, 23, 28) for stirring the reaction product at the reaction temperature and pressure in one or more segments of the tubular vessel (30) covering a sector of the reactor before its end area for exit towards the depressurization tank (21).