The problem of mass transfer in one-side-closed conical capillaries immersed in liquids is studied in this paper, The filling of such capillaries with liquids is characterized by the following specific feature : under certain conditions a capillary fills with a liquid both from the channel’s entrance and from its closed top. New peculiarities of double-side filling of conical capillaries with bidistilled water and ethanol have been established in this study. Some experimental results clarifying the physical nature of the phenomenon are obtained.