For leak testing closed containers (9) which are filled with a filling product containing at least one liquid component, the container is introduced in a test cavity (1) which is evacuated at least down to vapour pressure of that liquid component. The pressure in the surrounding of the container (9) and thus within test cavity (1) is monitored. Monitoring is performed by a vacuum pressure sensor (7), whereas lowering pressure surrounding the container (9) is performed by a vacuum pump (5). Leakage is detected by monitoring a pressure change in the surrounding of the container which is due to evaporation of liquid emerging from a leak and being evaporated in the low pressure surrounding.