Method for desalinating water comprises evaporating salt water under reduced pressure in an evaporation unit (10) and condensing it under reduced pressure in a condensing unit (23). The units are independently filled with salt water and pure water and the pressure in them is reduced before they are connected. An Independent claim is included for apparatus for carrying out the method comprising pump systems (3, 25) connected to working chambers (9, 27) which are in turn connected to the evaporation and condensing units and can be enlarged to reduce pressure in them. A shut-off valve (48) on the line (47) connecting the units opens when the working chambers are at their maximum volume.