Abstract: A method for distilling a fluid which is useful, for instance, in eliminating salt from brackish and/or sea water includes percolating films on plates with multiple effects having several evaporating zones and condensation zones. The evaporation zones (EVAP) and the condensation zones (COND) are vertically arranged. The liquid to be distilled emerges in the top part of the evaporation zone (EVAP). The vapors produced in the evaporation zone (EVAP) are horizontally transferred into the condensation zone (COND) through a communicating connection. The condensed liquid percolates vertically along the walls of the condensation zone and is evacuated from the lower part of the condensation zone. A distilling plant is also provided for implementing the distilling method, and includes plural cascades made up of elementary cells alternatingly assembled in thermal series.